Levelling up: How to unlock ecological and evolutionary data with hierarchical - Supplementary Material

Authors
Affiliations

Camille Lévesque

Université Laval

Katherine Hébert

McGill University

Laurence Feyten

Université du Québec à Montréal

Isabelle Lebeuf-Taylor

University of Alberta

Kim Ménard

Université TÉLUQ

Pedro Henrique Pereira Braga

McGill University

Alejandro Sepúlveda-Correa

Université du Québec en Outaouais

Aliénor Stahl

Université du Québec à Trois-Rivières

Lukas Van Riel

Université de Montréal

Published

November 7, 2025

1 Overview

This document provides the detailed code and supplementary materials for the article “Levelling up: How to unlock ecological data with hierarchical generalized additive models.”

It is divided as so:

  • Supplementary Material 1: Description of the data used throughout the study and across all coding examples (Boxes).

  • Supplementary Material 2: Code for Box 1 (Trends), corresponding to the section Estimating a hierarchy of trends in the article.

  • Supplementary Material 3: Code for Boxes 2 (Variance) and 3 (Prediction), which correspond respectively to the sections Unpacking meaningful variance and covariances from noisy biological data and Borrowing strength to boost predictions.

Most of the code presented here builds upon the examples and model structures introduced in Pedersen et al. (2019) and the various blog posts of Nicholas Clark (https://ecogambler.netlify.app/blog/).

2 Supplementary Material 1

2.1 Description of the data

We use the North American Breeding Bird Survey dataset extracted from BioTIME (Pardieck et al., 2015), a long-term monitoring program of North American bird populations that began in 1966. Our analyses focus on two subsets of the original dataset:

  • data_195: It is a cleaned subset of the original BioTIME data, containing only the 309 species with consistent observations between 1978 and 2007 (see Supplementary Material 2).
  • d_crop: It is a spatially cropped subset of data_195, containing only observations from Waverly, New York (latitude 44.55, longitude −74.4833). To create this localized dataset, non-essential columns were removed, and records were filtered to retain only species with complete 30-year time series at this site. One species (Vireo olivaceus) was further excluded due to inconsistent data (see Supplementary Material 3).

Table S1 presents the species used in the different coding examples (Boxes), which vary from one box to another according to the objectives and requirements of each example.

Table S1. Bird species and their inclusion (indicated by tick marks) in the coding examples presented in Boxes 1, 2, and 3. Box 1 uses the broader dataset (data_195), which includes randomly selected species from the North American Breeding Bird Survey as curated in BioTIME (Pardieck et al., 2015; Dornelas et al., 2018). Boxes 2 and 3 use the spatially cropped dataset (d_crop), restricted to observations from Waverly, New York (latitude 44.55, longitude −74.4833) collected between 1978 and 2007, and feature a subset of the most common species.Altogether, 36 bird species are represented across the three boxes.

Box
Common name Species name 1 2 3
Red-winged blackbird Agelaius phoeniceus x x x
Northern cardinal Cardinalis cardinalis x
Hermit thrush Chaetura pelagica x x
Chimney swift Chaetura pelagica x
Northern flicker Colaptes auratus x
Rock pigeon Columba livia x
Eastern wood-pewee Contopus virens x
American crow Corvus brachyrhynchos x
Blue jay Cyanocitta cristata x
Downy woodpecker Dryobates pubescens x
Gray catbird Dumetella carolinensis x
Common yellowthroat Geothlypis trichas x
Barn swallow Hirundo rustica x
Song sparrow Melospiza melodia x x x
Black-and-white warbler Mniotilta varia x x
Brown-headed cowbird Molothrus ater x
Great crested flycatcher Myiarchus crinitus x
House sparrow Passer domesticus x
Indigo bunting Passerina cyanea x
Common grackle Quiscalus quiscula x
Eastern phoebe Sayornis phoebe x
Ovenbird Seiurus aurocapilla x x
Yellow-rumped warbler Setophaga coronata x x
Black-throated green warbler Setophaga virens x x
American goldfinch Spinus tristis x x x
Chipping sparrow Spizella passerina x
Field sparrow Spizella pusilla x
Eastern meadowlark Sturnella magna x
Common starling Sturnus vulgaris x
Brown trasher Toxostoma rufum x
Northern house wren Troglodytes aedon x
American robin Turdus migratorius x x x
Eastern kingbird Tyrannus tyrannus x
Red-eyed vireo Vireo olivaceus x
Blue-headed vireo Vireo solitarius x x
Mourning dove Zenaida macroura x

3 Supplementary Material 2 - Box 1

3.1 Step 1: Setting up the work environment

3.1.1 Packages and Libraries

Here, we install and load the packages required for the coding examples.

# install.packages("pacman")

pacman::p_load(mgcv, # For fitting Generalized Additive Models (GAMs) and Hierarchical GAMs
dplyr,           # For data manipulation 
ggplot2,         # For data visualization
tidyr,           # For reshaping and tidying data
mvtnorm,         # For working with multivariate normal and t-distributions
gratia,          # For visualizing and interpreting GAMs fitted with mgcv
here,            # For handling file paths relative to the project root
gridExtra,       # For arranging multiple ggplot2 plots into grids
mvgam,           # For fitting multivariate/State-Space GAMs and plotting model components
marginaleffects, # For obtaining marginal/average predictions from fitted models
tidyverse,       # For the full suite of tidy tools (read, wrangle, plot) in one load
cmdstanr)        # For fitting Stan models via CmdStan, backend for mvgam

3.1.2 Import the raw data

We import the raw BBS data downloaded from BioTIME.

df <- read.csv(here::here("data", "clean", "data_195.csv"))

3.1.3 Make a subset of the data (data_195)

This dataset is the subset used in the coding example presented in Box 1. It also serves as the source for the additional subset used in Boxes 2 and 3 (see Supplementary Material 3).

# Filter to years in common across many species
df_years = df |>
  group_by(valid_name) |>
  summarise("min_year" = min(YEAR),
            "max_year" = max(YEAR))
# Look for the most common minimum and maximum years
df_years$min_year |> table()

1978 
 309 
df_years$max_year |> table()

2007 
 309 
# 309 species to keep
sp_to_keep = df_years |> filter(min_year == 1978, max_year == 2007)

# Cut to species that have data between 1978 and 2007
data_195 = df |> filter(valid_name %in% sp_to_keep$valid_name)

3.2 Step 2: Structure the data for analysis

We process the data by selecting the 30 most abundant species for the analyses. For this Box, we use the

# Aggregating biomass data to get a yearly abundance for each species.
community_ts <- data_195 %>%
  filter(!is.na(YEAR) & !is.na(valid_name) & valid_name != "") %>%
  group_by(YEAR, valid_name) %>%
  summarise(ABUNDANCE = n(), .groups = 'drop') %>%
  rename(year = YEAR, species = valid_name, abundance = ABUNDANCE)

# Selecting the top 30 most frequently observed species (i.e., highest in abundance)
top_species <- community_ts %>% # Identify the top 30 species
  group_by(species) %>%
  summarise(total_abundance = sum(abundance)) %>%
  arrange(desc(total_abundance)) %>%
  slice_head(n = 30) %>%
  pull(species)

community_ts_subset <- community_ts %>% # Create a new table with only the top 30 species
  filter(species %in% top_species) %>%
  mutate(species = as.factor(species))

head(community_ts_subset) # The subset of data that we will use from this point on in this section (Box 1)
# A tibble: 6 × 3
   year species               abundance
  <int> <fct>                     <int>
1  1978 Agelaius phoeniceus         406
2  1978 Cardinalis cardinalis       279
3  1978 Chaetura pelagica           284
4  1978 Colaptes auratus            342
5  1978 Columba livia               246
6  1978 Contopus virens             276

3.3 Step 3: Fit Model GS

Here, we fit the “GS” model described in Pedersen et al. (2019). Since the response variable represents abundance (count) data, we use the Poisson family.

# MODEL: The 'GS' Model (Global smooth + species-specific deviations)
gam_model_GS <- gam(
  # Global relationship
  abundance ~ s(year, bs = "tp") + 
    
  # Species-specific smoother: a factor-smoother interaction of year and species
  s(year, by = species, bs = "fs") + 
    
  # Species as random effects (gives an intercept per species)
  s(species, bs="re"), 
  
  # Data
  data = community_ts_subset,
  
  # Distribution family: Poisson for count data
  family = poisson(), 
  
  # Estimating smoothing parameters using restricted maximum likelihood (REML)
  method = "REML"
)

3.4 Step 4: Derivatives and Indicators

In this section, we generate predictions and calculate community-level indicators from the fitted GS model. We first create a prediction dataset covering all species and years, and use a small value (ε) to approximate derivatives numerically. We then draw 250 posterior simulations from the model coefficients to account for parameter uncertainty. Using these simulations, we compute predicted abundances and their first derivatives, which are used to estimate per capita rates of change. Finally, we summarize these results to obtain three community indicators for each year: the mean rate of change, the mean per capita rate of change, and the standard deviation of per capita rates of change, along with their median and 95% confidence intervals.

# Create a prediction dataset
predict_data <- community_ts_subset %>%
  select(year, species) %>%
  distinct()

# Define a small number 'eps' for numerical differentiation
eps <- 1e-7 # Define a small number epsilon ε 'eps'
predict_data_p_eps <- predict_data %>% mutate(year = year + eps)
predict_data_m_eps <- predict_data %>% mutate(year = year - eps)

# Generate posterior simulations from the GS model
n_sim <- 250
set.seed(42)
sim_lp_GS <- predict(gam_model_GS, newdata = predict_data, type = "lpmatrix")
sim_coef_GS <- rmvnorm(n_sim, coef(gam_model_GS), vcov(gam_model_GS, unconditional = TRUE))

# Calculate predicted values and derivatives for the GS model
pred_original_GS <- exp(sim_lp_GS %*% t(sim_coef_GS))
pred_p_eps_GS <- exp(predict(gam_model_GS, newdata = predict_data_p_eps, type = "lpmatrix") %*% t(sim_coef_GS))
pred_m_eps_GS <- exp(predict(gam_model_GS, newdata = predict_data_m_eps, type = "lpmatrix") %*% t(sim_coef_GS))
first_derivative_GS <- (pred_p_eps_GS - pred_m_eps_GS) / (2 * eps)
per_capita_rate_GS <- first_derivative_GS / (pred_original_GS + 1e-9)

# Reshape simulation results for the GS model
sim_deriv_long_GS <- as.data.frame(first_derivative_GS) %>%
  mutate(row = 1:n()) %>%
  pivot_longer(-row, names_to = "sim_id", values_to = "derivative")
sim_per_capita_long_GS <- as.data.frame(per_capita_rate_GS) %>%
  mutate(row = 1:n()) %>%
  pivot_longer(-row, names_to = "sim_id", values_to = "per_capita_rate")

sim_results_GS <- predict_data %>%
  mutate(row = 1:n()) %>%
  left_join(sim_deriv_long_GS, by = "row") %>%
  left_join(sim_per_capita_long_GS, by = c("row", "sim_id"))

# Calculate community indicators for the GS model
community_indicators_GS <- sim_results_GS %>%
  group_by(year, sim_id) %>%
  summarise(
    mean_rate_of_change = mean(derivative, na.rm = TRUE),
    mean_per_capita_rate = mean(per_capita_rate, na.rm = TRUE),
    sd_per_capita_rate = sd(per_capita_rate, na.rm = TRUE),
    .groups = 'drop'
  )

# Final summary of indicators for the GS model
final_indicators_GS <- community_indicators_GS %>%
  group_by(year) %>%
  summarise(
    across(
      .cols = c(mean_rate_of_change, mean_per_capita_rate, sd_per_capita_rate),
      .fns = list(
        median = ~median(.x, na.rm = TRUE),
        lower_ci = ~quantile(.x, 0.025, na.rm = TRUE),
        upper_ci = ~quantile(.x, 0.975, na.rm = TRUE)
      ),
      .names = "{.col}_{.fn}"
    ),
    .groups = 'drop'
  ) %>%
  mutate(model_type = "GS Model") # Add a label for plotting

3.4.1 Indicators from model GS

HGAMs offer an indicator-based approach using nonparametric spatiotemporal regression models to identify periods of change in community abundance or composition (i.e., regime shifts). This method estimates three key indicators: 1) the mean rate of change across all species, 2) the mean per-capita rate of change, and 3) the standard deviation of per-capita rates of change (Pedersen et al., 2020).

  1. The mean rate of change across all species

    This indicator represents the average temporal rate of change in abundance across all species in the community. It provides a general measure of whether the community as a whole is increasing or decreasing in total abundance over time.

  2. The mean per-capita rate of change

    This indicator expresses the average rate of change per individual, capturing the community’s relative growth or decline independently of overall abundance. It is analogous to the population growth rate at the individual level and reflects how efficiently individuals contribute to population change through time.

  3. The standard deviation of per-capita rates of change

    This indicator quantifies the variability in per-capita rates of change among species. High values suggest that species respond differently to environmental or ecological drivers, indicating potential desynchronization or restructuring within the community, which can signal the onset of regime shifts.

(head(final_indicators_GS))
# A tibble: 6 × 11
   year mean_rate_of_change_median mean_rate_of_change_…¹ mean_rate_of_change_…²
  <int>                      <dbl>                  <dbl>                  <dbl>
1  1978                      1.91                 -0.402                    4.12
2  1979                      1.84                 -0.367                    3.93
3  1980                      1.68                 -0.0327                   3.27
4  1981                      1.37                  0.137                    2.43
5  1982                      1.10                 -0.0447                   2.40
6  1983                      0.911                -0.291                    2.12
# ℹ abbreviated names: ¹​mean_rate_of_change_lower_ci,
#   ²​mean_rate_of_change_upper_ci
# ℹ 7 more variables: mean_per_capita_rate_median <dbl>,
#   mean_per_capita_rate_lower_ci <dbl>, mean_per_capita_rate_upper_ci <dbl>,
#   sd_per_capita_rate_median <dbl>, sd_per_capita_rate_lower_ci <dbl>,
#   sd_per_capita_rate_upper_ci <dbl>, model_type <chr>

3.5 Step 5: Plot the indicators

Here, we plot the three derivative-based indicators (mean rate of change, mean per capita rate, and the standard deviation of per capita rates) across years.

# Plot 1: Mean Rate of Change 
plot1_mean_rof <- ggplot(final_indicators_GS, 
                         aes(x = year)) +
  geom_ribbon(aes(ymin = mean_rate_of_change_lower_ci, 
                  ymax = mean_rate_of_change_upper_ci), 
              alpha = 0.8, fill = "#8fbcbb") +
  geom_line(aes(y = mean_rate_of_change_median), linewidth = 1) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  labs(
    title = "",
    y = "Mean rate of change\n(Abundance / Year)", x = "Year",
  ) + 
  ggpubr::theme_pubr() +
  theme(panel.grid.major = element_line(linewidth = .3))

# Plot 2: Mean Per-Capita Rate of Change 
plot2_mean_percap_rof <- ggplot(final_indicators_GS, 
                                aes(x = year)) +
  geom_ribbon(aes(ymin = mean_per_capita_rate_lower_ci, 
                  ymax = mean_per_capita_rate_upper_ci), 
              alpha = 0.8, fill = "#88c0d0") +
  geom_line(aes(y = mean_per_capita_rate_median), linewidth = 1) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  labs(
    title = "",
    y = "Mean per-capita\nrate of change", x = "Year",
  ) + 
  ggpubr::theme_pubr() +
  theme(panel.grid.major = element_line(linewidth = .3))

# Plot 3: SD of Per-Capita Rates 
plot3_SD_percap_rof <- ggplot(final_indicators_GS, 
                              aes(x = year)) +
  geom_ribbon(aes(ymin = sd_per_capita_rate_lower_ci, 
                  ymax = sd_per_capita_rate_upper_ci), 
              alpha = 0.6, fill = "#5e81ac") +
  geom_line(aes(y = sd_per_capita_rate_median), linewidth = 1) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  labs(
    title = "",
    y = "SD of per-capita\nrates of change", x = "Year",
  ) + 
  ggpubr::theme_pubr()+
  theme(panel.grid.major = element_line(linewidth = .3))

# Print the plots
print(plot1_mean_rof)

print(plot2_mean_percap_rof)

print(plot3_SD_percap_rof)

3.5.1 Making a figure with the plots of indicators

Here, we create the figure that displays the three derivative-based indicators. This figure corresponds to Box 1 in the paper (i.e., Figure 3).

library(patchwork)
plot1_mean_rof + plot2_mean_percap_rof + plot3_SD_percap_rof + plot_annotation(tag_levels = "a")

4 Supplementary Material 3 - Boxes 2 & 3

In this section, we present the coding examples from Boxes 2 (Variance) and 3 (Prediction), both of which use the same data subset (d_crop) from Waverly, New York.

4.1 Step 1: Setting up the work environment

4.1.1 Make a subset of the data (d_crop)

The dataset is cropped to include only observations from the Waverly, New York region, and the Red-eyed vireo (Vireo olivaceus) is removed due to inconsistent data.

df = df |>
  select(-c(SAMPLE_DESC, DAY, MONTH, BIOMAS))

sites = paste0(df$LONGITUDE,"_", df$LATITUDE)
table(sites)
sites
-100.483_37.3167  -102.25_35.7333 -103.367_47.2167 -103.633_43.8167 
             988             1170             1201             1233 
-103.667_39.8667    -105.067_40.5  -105.65_52.7333 -105.733_42.8167 
             696             1364             1142              818 
  -105.8_36.0833     -105.85_53.1 -106.067_35.5167 -106.117_42.8667 
            1700             1197             1044             1241 
   -106.117_51.4 -106.717_44.8833 -107.667_39.9833    -107.85_52.25 
             936             1127             1604             1518 
   -107.983_38.3 -108.967_31.8333     -109.45_45.7   -110.3_32.0333 
            1497              871             1755             1466 
  -110.8_31.5167   -111.8_45.8833  -111.85_50.5667 -112.267_44.2333 
            1834             1411              968              714 
-112.383_34.6667   -112.483_42.85     -112.8_43.15 -113.367_44.7833 
            2064              979             1018             1124 
-113.467_43.4167      -113.567_45     -113.65_46.7    -114.167_47.7 
             867             1325             1272             1216 
  -114.217_44.55 -114.467_48.1167 -114.483_52.0167  -114.75_54.0833 
            1155             1809             1333             1383 
 -115.15_47.3667 -115.617_40.0667 -117.217_45.2833    -118.133_36.5 
            1326              819             1338             1106 
-118.333_49.9833     -118.5_48.05   -119.283_36.65    -119.367_37.3 
            1639             1635             1627             1600 
   -119.717_49.6 -119.733_48.0833    -120.25_40.85    -120.45_38.85 
            2124             1059             1084             1580 
   -120.667_51.4 -120.833_37.5833  -120.85_39.5667   -120.933_38.75 
            1458             1159             1421             1762 
  -121.017_39.05   -121.1_41.8333   -121.217_48.75    -121.267_41.1 
            1415             1149             1553             1762 
   -121.583_40.8   -121.583_46.35    -121.617_39.6   -121.667_36.45 
            1313             1550             1101             1908 
  -121.8_42.3667   -121.9_41.9833   -122.067_39.55 -122.067_52.1667 
            1363             1394              944             1399 
   -122.15_41.85  -122.25_39.7667   -122.3_40.8833 -122.333_48.1333 
            2047              973             1437             1461 
  -122.667_41.75 -122.717_38.5667   -122.8_53.9333 -123.067_41.9167 
            1752             1632             1477             1576 
-123.233_42.9333 -123.383_48.1167     -123.5_43.35    -123.617_38.8 
            1598             1538             1725             1969 
-123.667_42.4167   -124.4_42.5167 -124.667_48.1167   -61.5667_45.15 
            1637             1124             1207             1397 
   -62.6_44.9333 -65.7167_45.6333   -65.95_45.7167 -68.9167_47.9333 
            1365             2081             1702             1784 
  -69.45_44.9833 -69.5667_43.9833    -70.5333_43.5   -70.5667_44.15 
            1616             1568             1813             1796 
  -70.6167_47.65   -70.6667_43.25   -70.7167_43.15 -70.9167_43.2333 
            1243             1378             1253             1752 
-71.1333_46.0167       -71.3_43.2      -71.3667_45    -71.4667_46.7 
            1662             1741             1848             1477 
   -71.5667_44.7 -71.7167_44.1667   -71.75_43.3667 -71.8667_42.8833 
            1732             2074             1674             1771 
-71.9333_43.4333 -72.1333_41.7667    -72.1667_42.8    -72.2_43.0667 
            1803             1694             1890             1886 
-72.2833_42.6167   -72.35_42.2667    -72.4_43.0167 -72.4667_42.2167 
            1909             1833             1742             1876 
   -72.5167_41.7   -72.5833_45.95     -72.85_42.35    -72.9_42.4667 
            1489             1632             1937             1894 
-73.1833_42.4167   -73.2167_41.55   -73.3333_41.75 -73.3333_45.0833 
            1708             1824             2084             1214 
   -73.4_45.7167    -73.4167_42.1    -73.5_41.5333    -73.5_42.3333 
            1606             2075             1869             1732 
  -73.9833_41.75 -74.0667_45.7833   -74.1833_44.45 -74.3333_41.9833 
            1697             1907             1787             1928 
  -74.4833_44.55 -74.9167_40.4667    -75.1_40.6667    -75.1167_39.5 
            1847             1673             1532             1351 
  -75.2333_41.55   -75.25_38.2333     -75.25_41.35 -75.3667_40.8167 
            2099             1744             1990             1319 
-75.4667_39.0333   -75.4667_40.15   -75.5333_38.95 -75.5833_38.1667 
            1561             1405             1861             1732 
   -75.6833_39.5 -75.7667_39.2667   -75.7833_38.55    -75.7833_41.7 
            1615             1886             1713             1905 
-75.8833_38.7833      -75.9_43.45 -75.9167_39.5167 -75.9333_38.8833 
            1712             1831             1815             1769 
  -75.9333_42.35 -75.9667_40.8167      -76_39.6167   -76.0167_46.35 
            1752             1904             1879             1719 
  -76.0333_42.35    -76.1_45.5667   -76.15_39.2667 -76.1667_38.2667 
            1692             1810             1818             1923 
   -76.1833_39.1 -76.2167_38.5333   -76.25_38.4667 -76.2833_36.6167 
            1902             1978             1583             1631 
     -76.3_39.45 -76.4333_41.2167 -76.4833_39.5333    -76.5167_41.1 
            1595             1944             1533             1838 
  -76.6333_42.55   -76.6667_34.95 -76.6833_37.8667    -76.7167_40.2 
            1690             1883             1750             1434 
   -76.7333_39.7   -76.8167_39.55   -76.85_39.0167 -76.9667_38.4833 
            1741             1649             1556             1723 
-76.9667_39.7333   -76.9833_36.35 -77.0333_39.5167   -77.0333_39.65 
            1809             2020             1708             1709 
     -77.05_38.6   -77.0667_44.35 -77.0833_38.6333   -77.0833_39.15 
            1784             2505             1674             1996 
   -77.1167_42.9 -77.1667_41.6667   -77.35_44.0667    -77.4_40.5833 
            1812             1689             1586             1603 
-77.4167_35.9833 -77.4667_45.2833 -77.5167_40.6833   -77.55_39.5833 
            1875             1752             1600             1929 
   -77.7167_35.3     -77.85_39.65      -77.85_42.5      -77.95_42.2 
            1588             1721             2096             1843 
     -77.95_42.7   -77.9833_36.25 -78.0833_42.6167 -78.1833_40.5833 
            1765             1956             1573             1727 
   -78.3667_42.6 -78.4833_39.1833     -78.55_38.55 -78.5667_38.8167 
            1432             1769             1605             1559 
-78.5833_42.0833    -78.6833_37.9       -78.8_37.7 -78.8167_39.6167 
            1583             1906             1837             1848 
-78.8333_42.0667 -78.9667_39.7833   -78.9833_43.25      -79_41.6167 
            1885             1840             1550             1568 
-79.0667_39.8833 -79.1333_39.4333      -79.15_38.2 -79.1833_44.3167 
            1845             2015             1699             1729 
-79.2333_40.6667   -79.25_39.2167   -79.25_40.6333   -79.35_41.5167 
            1847             1552             1814             1672 
  -79.6333_37.65     -79.65_39.65     -79.75_43.55    -79.8333_39.6 
            1570             1506             1655             1427 
-79.9333_39.0833   -80.05_37.7833 -80.3333_38.7167   -80.35_40.1667 
            1626             1683             1633             1683 
  -80.75_39.9333   -80.7833_39.65 -80.7833_41.6333   -80.9167_43.15 
            1811             1928             1657             1386 
-80.9833_41.3167    -81.2167_44.3    -81.3833_27.3    -81.4833_26.3 
            1568             1302             1149              855 
-81.7333_32.5833    -81.8_38.5667    -81.8_45.7167 -81.8167_29.8333 
            1525             1728             1801             1252 
-81.8833_39.2667   -81.95_37.0167   -81.9833_28.55   -82.15_27.6667 
            1644             1436             1228             1154 
-82.1667_39.3333 -82.2167_33.5167      -82.25_30.2   -82.2833_39.25 
            1628             1652             1280             1680 
   -82.3_28.3167    -82.5_37.2333   -82.6333_33.65   -83.2833_34.65 
            1349             1841             1739             1734 
-83.4167_38.6667    -83.4833_32.4    -83.5833_33.6    -83.8167_33.1 
            1787             1558             1710             1587 
  -83.8833_30.65 -83.9167_30.1833   -83.95_38.2167 -84.0333_30.5833 
            1503             1529             1778             1389 
  -84.15_35.9167 -84.1667_38.4333 -84.2167_33.6333    -84.2833_32.2 
            1496             1623             1649             1529 
-84.3167_36.5333   -84.35_46.2167 -84.3667_36.0667 -84.4167_36.2833 
            1875             1562             1950             2026 
-84.4167_41.8167    -84.6_38.3667   -84.75_37.3333   -84.85_40.6833 
            1519             1691             1660             1340 
   -84.9_29.9833 -85.1333_37.4333   -85.25_33.5333    -85.3_29.7833 
            1232             1981             1729             1289 
     -85.35_35.1   -85.4167_42.25      -85.55_32.3   -85.65_35.1833 
            1728             1759             1599             1731 
   -85.7667_36.1 -85.7667_41.9667 -85.9167_35.3833 -86.1333_42.5167 
            1823             1671             1581             1983 
-86.1833_35.7333 -86.2333_34.8667 -86.2333_43.8833   -86.25_31.5833 
            1816             1337             1587             1510 
     -86.6_31.45    -86.6_33.4667 -86.6167_36.9667      -86.65_36.5 
            1731             1811             1637             1484 
-86.6667_35.3333 -86.8333_35.8333      -87_33.5333    -87.1_33.1333 
            1624             1499             1740             1562 
  -87.15_39.5667      -87.2_31.75   -87.2167_32.45 -87.3333_35.8667 
            1368             1700             1663             2014 
  -87.35_40.6667 -87.5333_32.7833 -87.6833_35.4833   -87.7333_40.65 
            1581             1729             2007             1255 
-87.7833_39.3333   -87.8833_43.35 -87.8833_45.3667 -87.9833_42.7833 
            1282             1614             2036             1431 
-88.0333_42.6333       -88.1_39.9 -88.1667_44.8667 -88.1833_41.1667 
            1662             1291             2344              873 
   -88.2_33.4833       -88.2_36.7    -88.2_39.3167 -88.2333_38.2167 
            1765             1719             1548             1558 
-88.2667_39.3667   -88.3333_32.15   -88.35_43.6667 -88.3833_39.6167 
            1157             1756             1640             1220 
-88.5167_31.6667 -88.5167_37.0667 -88.5333_35.3833   -88.55_40.0833 
            1338             1988             1496             1088 
  -88.6833_44.05   -88.75_45.4833    -88.8_35.3667    -88.8_44.6167 
            1984             2102             1629             1994 
  -88.95_37.3167   -88.95_40.9333   -88.95_44.4167   -89.0167_41.65 
            1853             1106             2476             1030 
   -89.0333_44.2 -89.0833_35.3667 -89.0833_42.0667   -89.1833_43.55 
            1805             1657             1467             1936 
-89.1833_45.9333       -89.2_39.4   -89.25_37.2333 -89.2833_44.7333 
            2029             1061             1937             1728 
-89.3333_35.6833 -89.3333_42.1667   -89.3667_35.55    -89.3667_36.3 
            1371             1625             1297             1437 
-89.4333_36.4167     -89.45_39.55      -89.45_41.2    -89.5167_37.3 
            1743             1240             1268             1454 
-89.6167_45.3167    -89.6333_40.6 -89.6333_46.1833   -89.75_37.9667 
            1985             1384             1812             1787 
   -89.8_40.9333 -89.8167_38.5333 -89.8833_43.4333 -90.0333_40.9167 
            1307             1592             1851             1472 
  -90.05_44.6167 -90.0667_45.3333 -90.1667_39.4333    -90.2_45.6333 
            1313             1893             1604             2117 
   -90.3_41.9667 -90.3167_43.7333 -90.3667_44.2167    -90.3833_44.8 
            1454             1841             1833             1702 
    -90.45_37.25    -90.5_34.9333    -90.5_40.8667   -90.5833_42.05 
            1968             1288             1053             1433 
-90.6667_35.5333 -90.6833_47.7333   -90.95_46.8333   -90.9833_40.65 
            1202             1289             1963             1616 
   -91.0667_46.3 -91.1833_40.2167      -91.35_35.9 -91.4167_44.0167 
            1793             1503             1438             1735 
     -91.45_37.9    -91.5_47.6833 -91.5833_37.3667    -91.8_47.0667 
            1740             1440             1837             1676 
-91.8333_30.0667    -92.2_35.5667 -92.2333_46.3167   -92.25_45.6333 
            1081             1654             2121             2118 
  -92.45_38.5667    -92.5_45.9667   -92.6333_34.35    -92.7_33.5833 
            1716             1581             1829             1786 
   -92.7_45.3833 -92.7167_35.6333   -92.85_38.2833   -92.8667_40.65 
            1931             1694             1861             1444 
-93.0667_35.8167   -93.15_40.8833     -93.25_34.05    -93.2833_36.1 
            1579             1370             1730             1785 
  -93.3333_44.65 -93.4667_44.9667 -93.4833_33.3667    -93.5_43.8167 
            1508             1546             1648             1177 
   -93.5_45.5667   -93.5167_37.45    -93.6_35.4167 -93.6333_47.3333 
            1827             1499             1602             1481 
-93.6833_33.6667    -94.0167_43.2 -94.0667_34.9833   -94.0833_41.75 
            1552             1152             1044             1307 
   -94.1167_36.4   -94.1167_37.15    -94.1333_33.7    -94.2_45.1667 
            1442             1452             1522             1531 
  -94.25_49.7167 -94.5167_31.8833   -94.85_31.1833 -94.8667_35.8167 
            1866             1663             1504             2069 
      -94.9_38.8    -94.9333_30.7 -95.1333_36.9167   -95.4667_46.75 
            1589             1462             1380             1763 
     -95.6_39.25    -95.6167_28.9   -95.6167_39.05   -95.7833_38.45 
            1414             1136             1631             1564 
   -95.8667_31.8    -95.8833_38.9 -96.0167_39.7167 -96.0667_41.1667 
            1261             1729             1659             1186 
  -96.0833_41.35 -96.3833_42.4667    -96.5_38.3167 -96.7167_49.7167 
            1395             1344             1321             1322 
-96.7667_38.9167 -96.8833_39.8833   -96.95_44.2333 -97.1833_34.1333 
            1728             1410             1244             1316 
  -97.2667_33.55   -97.35_41.1667    -97.4_47.9667 -97.4333_35.1833 
            1229              971             1607             1667 
  -97.4667_43.95    -97.7_26.5333 -98.0167_49.3833   -98.05_32.1667 
            1231              931             1426             1120 
  -99.1833_30.35 -99.2167_37.2167 -99.5667_39.6833    -99.9833_50.2 
            1187             1320              985             1167 
# crop to a site
d_crop = df[sites %in% "-74.4833_44.55",] # We keep sites in Waverly, New York

## crop to birds 
species = table(d_crop$valid_name)
species = species[which(species == 30)]
ex = names(species)

d_crop = dplyr::filter(d_crop, valid_name %in% ex)
d_crop = dplyr::filter(d_crop, valid_name != "Vireo olivaceus")

4.2 Step 2: Data exploration

# summarise data contents
dls = d_crop |>
  group_by(valid_name) |>
  group_split()

# check for basic population trends
mls = lapply(dls, function(x){lm(ABUNDANCE ~ YEAR, data = x)})

# extract slopes
coefs = mls |> lapply(coef) |> 
  bind_rows() |> 
  mutate("species" = unique(d_crop$valid_name))

# plot to see the slopes
ggplot(data = coefs) +
  geom_point(aes(y = species, x = YEAR))

4.3 Step 3: Box 2 - Variance

4.3.1 Build a model for each species

# check for basic population trends
gamls = lapply(dls, function(x){gam(ABUNDANCE ~ s(YEAR, k = 4), data = x)})
lapply(gamls, plot)

[[1]]
[[1]][[1]]
[[1]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[1]][[1]]$scale
[1] TRUE

[[1]][[1]]$se
  [1] 11.917084 11.301201 10.695914 10.103460  9.526369  8.967671  8.430857
  [8]  7.919777  7.438676  6.992187  6.585134  6.222323  5.908240  5.646592
 [15]  5.439779  5.288406  5.190961  5.143721  5.141007  5.175787  5.240271
 [22]  5.326468  5.426800  5.534432  5.643283  5.748147  5.844854  5.929987
 [29]  6.000775  6.055263  6.092139  6.110505  6.109987  6.090822  6.053571
 [36]  5.999125  5.928916  5.844733  5.748622  5.643030  5.530807  5.415024
 [43]  5.298980  5.186265  5.080538  4.985402  4.904329  4.840452  4.796325
 [50]  4.773776  4.773776  4.796325  4.840452  4.904329  4.985402  5.080538
 [57]  5.186265  5.298980  5.415024  5.530807  5.643030  5.748622  5.844733
 [64]  5.928916  5.999125  6.053571  6.090822  6.109987  6.110505  6.092139
 [71]  6.055263  6.000775  5.929987  5.844854  5.748147  5.643283  5.534432
 [78]  5.426800  5.326468  5.240271  5.175787  5.141007  5.143721  5.190961
 [85]  5.288406  5.439779  5.646592  5.908240  6.222323  6.585134  6.992187
 [92]  7.438676  7.919777  8.430857  8.967671  9.526369 10.103460 10.695914
 [99] 11.301201 11.917084

[[1]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[1]][[1]]$xlab
[1] "YEAR"

[[1]][[1]]$ylab
[1] "s(YEAR,2.85)"

[[1]][[1]]$main
NULL

[[1]][[1]]$se.mult
[1] 2

[[1]][[1]]$xlim
[1] 1978 2007

[[1]][[1]]$fit
              [,1]
  [1,]   7.6407932
  [2,]   6.9492547
  [3,]   6.2588084
  [4,]   5.5705463
  [5,]   4.8855848
  [6,]   4.2054225
  [7,]   3.5318632
  [8,]   2.8667195
  [9,]   2.2119042
 [10,]   1.5695711
 [11,]   0.9419096
 [12,]   0.3311141
 [13,]  -0.2605788
 [14,]  -0.8309116
 [15,]  -1.3776279
 [16,]  -1.8985468
 [17,]  -2.3916013
 [18,]  -2.8547337
 [19,]  -3.2859430
 [20,]  -3.6835075
 [21,]  -4.0457911
 [22,]  -4.3711713
 [23,]  -4.6583154
 [24,]  -4.9061674
 [25,]  -5.1136824
 [26,]  -5.2799729
 [27,]  -5.4046138
 [28,]  -5.4872644
 [29,]  -5.5276259
 [30,]  -5.5258439
 [31,]  -5.4823338
 [32,]  -5.3975175
 [33,]  -5.2720686
 [34,]  -5.1071161
 [35,]  -4.9038370
 [36,]  -4.6634831
 [37,]  -4.3877614
 [38,]  -4.0785501
 [39,]  -3.7377367
 [40,]  -3.3674746
 [41,]  -2.9702223
 [42,]  -2.5484548
 [43,]  -2.1047305
 [44,]  -1.6419081
 [45,]  -1.1629138
 [46,]  -0.6706851
 [47,]  -0.1683110
 [48,]   0.3410093
 [49,]   0.8540736
 [50,]   1.3676566
 [51,]   1.8784823
 [52,]   2.3832676
 [53,]   2.8787398
 [54,]   3.3617013
 [55,]   3.8289888
 [56,]   4.2774421
 [57,]   4.7040271
 [58,]   5.1058822
 [59,]   5.4801584
 [60,]   5.8240800
 [61,]   6.1351965
 [62,]   6.4111476
 [63,]   6.6495909
 [64,]   6.8485067
 [65,]   7.0061577
 [66,]   7.1208164
 [67,]   7.1909344
 [68,]   7.2154404
 [69,]   7.1933413
 [70,]   7.1236940
 [71,]   7.0060287
 [72,]   6.8401373
 [73,]   6.6258185
 [74,]   6.3631495
 [75,]   6.0526671
 [76,]   5.6949510
 [77,]   5.2906676
 [78,]   4.8409585
 [79,]   4.3471265
 [80,]   3.8104859
 [81,]   3.2326330
 [82,]   2.6154586
 [83,]   1.9608678
 [84,]   1.2708512
 [85,]   0.5476788
 [86,]  -0.2063224
 [87,]  -0.9888170
 [88,]  -1.7973631
 [89,]  -2.6294481
 [90,]  -3.4825584
 [91,]  -4.3542108
 [92,]  -5.2419819
 [93,]  -6.1434559
 [94,]  -7.0562569
 [95,]  -7.9782824
 [96,]  -8.9075427
 [97,]  -9.8420580
 [98,] -10.7801849
 [99,] -11.7207020
[100,] -12.6624140

[[1]][[1]]$plot.me
[1] TRUE



[[2]]
[[2]][[1]]
[[2]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[2]][[1]]$scale
[1] TRUE

[[2]][[1]]$se
  [1] 11.3301747 11.1012822 10.8723898 10.6434974 10.4146050 10.1857126
  [7]  9.9568202  9.7279277  9.4990353  9.2701429  9.0412505  8.8123581
 [13]  8.5834656  8.3545732  8.1256808  7.8967884  7.6678960  7.4390036
 [19]  7.2101111  6.9812187  6.7523263  6.5234339  6.2945415  6.0656491
 [25]  5.8367566  5.6078642  5.3789718  5.1500794  4.9211870  4.6922946
 [31]  4.4634021  4.2345097  4.0056173  3.7767249  3.5478325  3.3189401
 [37]  3.0900476  2.8611552  2.6322628  2.4033704  2.1744780  1.9455856
 [43]  1.7166931  1.4878007  1.2589083  1.0300159  0.8011235  0.5722311
 [49]  0.3433387  0.1144464  0.1144464  0.3433387  0.5722311  0.8011235
 [55]  1.0300159  1.2589083  1.4878007  1.7166931  1.9455856  2.1744780
 [61]  2.4033704  2.6322628  2.8611552  3.0900476  3.3189401  3.5478325
 [67]  3.7767249  4.0056173  4.2345097  4.4634021  4.6922946  4.9211870
 [73]  5.1500794  5.3789718  5.6078642  5.8367566  6.0656491  6.2945415
 [79]  6.5234339  6.7523263  6.9812187  7.2101111  7.4390036  7.6678960
 [85]  7.8967884  8.1256808  8.3545732  8.5834656  8.8123581  9.0412505
 [91]  9.2701429  9.4990353  9.7279277  9.9568202 10.1857126 10.4146050
 [97] 10.6434974 10.8723898 11.1012822 11.3301747

[[2]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[2]][[1]]$xlab
[1] "YEAR"

[[2]][[1]]$ylab
[1] "s(YEAR,1)"

[[2]][[1]]$main
NULL

[[2]][[1]]$se.mult
[1] 2

[[2]][[1]]$xlim
[1] 1978 2007

[[2]][[1]]$fit
              [,1]
  [1,]  3.64516129
  [2,]  3.57152166
  [3,]  3.49788204
  [4,]  3.42424242
  [5,]  3.35060280
  [6,]  3.27696318
  [7,]  3.20332355
  [8,]  3.12968393
  [9,]  3.05604431
 [10,]  2.98240469
 [11,]  2.90876507
 [12,]  2.83512545
 [13,]  2.76148582
 [14,]  2.68784620
 [15,]  2.61420658
 [16,]  2.54056696
 [17,]  2.46692734
 [18,]  2.39328772
 [19,]  2.31964809
 [20,]  2.24600847
 [21,]  2.17236885
 [22,]  2.09872923
 [23,]  2.02508961
 [24,]  1.95144998
 [25,]  1.87781036
 [26,]  1.80417074
 [27,]  1.73053112
 [28,]  1.65689150
 [29,]  1.58325188
 [30,]  1.50961225
 [31,]  1.43597263
 [32,]  1.36233301
 [33,]  1.28869339
 [34,]  1.21505377
 [35,]  1.14141414
 [36,]  1.06777452
 [37,]  0.99413490
 [38,]  0.92049528
 [39,]  0.84685566
 [40,]  0.77321603
 [41,]  0.69957641
 [42,]  0.62593679
 [43,]  0.55229717
 [44,]  0.47865755
 [45,]  0.40501792
 [46,]  0.33137830
 [47,]  0.25773868
 [48,]  0.18409906
 [49,]  0.11045944
 [50,]  0.03681981
 [51,] -0.03681981
 [52,] -0.11045943
 [53,] -0.18409905
 [54,] -0.25773867
 [55,] -0.33137830
 [56,] -0.40501792
 [57,] -0.47865754
 [58,] -0.55229716
 [59,] -0.62593678
 [60,] -0.69957641
 [61,] -0.77321603
 [62,] -0.84685565
 [63,] -0.92049527
 [64,] -0.99413490
 [65,] -1.06777452
 [66,] -1.14141414
 [67,] -1.21505376
 [68,] -1.28869338
 [69,] -1.36233301
 [70,] -1.43597263
 [71,] -1.50961225
 [72,] -1.58325187
 [73,] -1.65689149
 [74,] -1.73053112
 [75,] -1.80417074
 [76,] -1.87781036
 [77,] -1.95144998
 [78,] -2.02508961
 [79,] -2.09872923
 [80,] -2.17236885
 [81,] -2.24600847
 [82,] -2.31964809
 [83,] -2.39328772
 [84,] -2.46692734
 [85,] -2.54056696
 [86,] -2.61420658
 [87,] -2.68784621
 [88,] -2.76148583
 [89,] -2.83512545
 [90,] -2.90876507
 [91,] -2.98240469
 [92,] -3.05604432
 [93,] -3.12968394
 [94,] -3.20332356
 [95,] -3.27696318
 [96,] -3.35060281
 [97,] -3.42424243
 [98,] -3.49788205
 [99,] -3.57152167
[100,] -3.64516129

[[2]][[1]]$plot.me
[1] TRUE



[[3]]
[[3]][[1]]
[[3]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[3]][[1]]$scale
[1] TRUE

[[3]][[1]]$se
  [1] 6.98233708 6.84127976 6.70022245 6.55916513 6.41810782 6.27705050
  [7] 6.13599319 5.99493587 5.85387856 5.71282125 5.57176393 5.43070662
 [13] 5.28964930 5.14859199 5.00753467 4.86647736 4.72542004 4.58436273
 [19] 4.44330541 4.30224810 4.16119078 4.02013347 3.87907615 3.73801884
 [25] 3.59696152 3.45590421 3.31484690 3.17378958 3.03273227 2.89167495
 [31] 2.75061764 2.60956032 2.46850301 2.32744569 2.18638838 2.04533106
 [37] 1.90427375 1.76321643 1.62215912 1.48110180 1.34004449 1.19898718
 [43] 1.05792986 0.91687255 0.77581523 0.63475792 0.49370060 0.35264329
 [49] 0.21158597 0.07052866 0.07052866 0.21158597 0.35264329 0.49370060
 [55] 0.63475792 0.77581523 0.91687255 1.05792986 1.19898718 1.34004449
 [61] 1.48110180 1.62215912 1.76321643 1.90427375 2.04533106 2.18638838
 [67] 2.32744569 2.46850301 2.60956032 2.75061764 2.89167495 3.03273227
 [73] 3.17378958 3.31484690 3.45590421 3.59696152 3.73801884 3.87907615
 [79] 4.02013347 4.16119078 4.30224810 4.44330541 4.58436273 4.72542004
 [85] 4.86647736 5.00753467 5.14859199 5.28964930 5.43070662 5.57176393
 [91] 5.71282125 5.85387856 5.99493587 6.13599319 6.27705050 6.41810782
 [97] 6.55916513 6.70022245 6.84127976 6.98233708

[[3]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[3]][[1]]$xlab
[1] "YEAR"

[[3]][[1]]$ylab
[1] "s(YEAR,1)"

[[3]][[1]]$main
NULL

[[3]][[1]]$se.mult
[1] 2

[[3]][[1]]$xlim
[1] 1978 2007

[[3]][[1]]$fit
              [,1]
  [1,]  11.0677419
  [2,]  10.8441512
  [3,]  10.6205604
  [4,]  10.3969697
  [5,]  10.1733790
  [6,]   9.9497882
  [7,]   9.7261975
  [8,]   9.5026067
  [9,]   9.2790160
 [10,]   9.0554252
 [11,]   8.8318345
 [12,]   8.6082437
 [13,]   8.3846530
 [14,]   8.1610622
 [15,]   7.9374715
 [16,]   7.7138807
 [17,]   7.4902900
 [18,]   7.2666993
 [19,]   7.0431085
 [20,]   6.8195178
 [21,]   6.5959270
 [22,]   6.3723363
 [23,]   6.1487455
 [24,]   5.9251548
 [25,]   5.7015640
 [26,]   5.4779733
 [27,]   5.2543825
 [28,]   5.0307918
 [29,]   4.8072010
 [30,]   4.5836103
 [31,]   4.3600196
 [32,]   4.1364288
 [33,]   3.9128381
 [34,]   3.6892473
 [35,]   3.4656566
 [36,]   3.2420658
 [37,]   3.0184751
 [38,]   2.7948843
 [39,]   2.5712936
 [40,]   2.3477028
 [41,]   2.1241121
 [42,]   1.9005213
 [43,]   1.6769306
 [44,]   1.4533399
 [45,]   1.2297491
 [46,]   1.0061584
 [47,]   0.7825676
 [48,]   0.5589769
 [49,]   0.3353861
 [50,]   0.1117954
 [51,]  -0.1117954
 [52,]  -0.3353861
 [53,]  -0.5589769
 [54,]  -0.7825676
 [55,]  -1.0061584
 [56,]  -1.2297491
 [57,]  -1.4533399
 [58,]  -1.6769306
 [59,]  -1.9005213
 [60,]  -2.1241121
 [61,]  -2.3477028
 [62,]  -2.5712936
 [63,]  -2.7948843
 [64,]  -3.0184751
 [65,]  -3.2420658
 [66,]  -3.4656566
 [67,]  -3.6892473
 [68,]  -3.9128381
 [69,]  -4.1364288
 [70,]  -4.3600196
 [71,]  -4.5836103
 [72,]  -4.8072010
 [73,]  -5.0307918
 [74,]  -5.2543825
 [75,]  -5.4779733
 [76,]  -5.7015640
 [77,]  -5.9251548
 [78,]  -6.1487455
 [79,]  -6.3723363
 [80,]  -6.5959270
 [81,]  -6.8195178
 [82,]  -7.0431085
 [83,]  -7.2666993
 [84,]  -7.4902900
 [85,]  -7.7138807
 [86,]  -7.9374715
 [87,]  -8.1610622
 [88,]  -8.3846530
 [89,]  -8.6082437
 [90,]  -8.8318345
 [91,]  -9.0554252
 [92,]  -9.2790160
 [93,]  -9.5026067
 [94,]  -9.7261975
 [95,]  -9.9497882
 [96,] -10.1733790
 [97,] -10.3969697
 [98,] -10.6205604
 [99,] -10.8441512
[100,] -11.0677419

[[3]][[1]]$plot.me
[1] TRUE



[[4]]
[[4]][[1]]
[[4]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[4]][[1]]$scale
[1] TRUE

[[4]][[1]]$se
  [1] 14.869908 14.104611 13.352472 12.616253 11.899079 11.204685 10.537376
  [8]  9.901887  9.303439  8.747722  8.240658  7.788143  7.395683  7.067843
 [15]  6.807606  6.615778  6.490587  6.427564  6.419826  6.458808  6.534969
 [22]  6.638484  6.760001  6.891052  7.024086  7.152624  7.271458  7.376320
 [29]  7.463737  7.531254  7.577213  7.600475  7.600556  7.577727  7.532667
 [36]  7.466463  7.380876  7.278107  7.160672  7.031585  6.894355  6.752755
 [43]  6.610840  6.473010  6.343749  6.227461  6.128385  6.050340  5.996436
 [50]  5.968893  5.968893  5.996436  6.050340  6.128385  6.227461  6.343749
 [57]  6.473010  6.610840  6.752755  6.894355  7.031585  7.160672  7.278107
 [64]  7.380876  7.466463  7.532667  7.577727  7.600556  7.600475  7.577213
 [71]  7.531254  7.463737  7.376320  7.271458  7.152624  7.024086  6.891052
 [78]  6.760001  6.638484  6.534969  6.458808  6.419826  6.427564  6.490587
 [85]  6.615778  6.807606  7.067843  7.395683  7.788143  8.240658  8.747722
 [92]  9.303439  9.901887 10.537376 11.204685 11.899079 12.616253 13.352472
 [99] 14.104611 14.869908

[[4]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[4]][[1]]$xlab
[1] "YEAR"

[[4]][[1]]$ylab
[1] "s(YEAR,2.83)"

[[4]][[1]]$main
NULL

[[4]][[1]]$se.mult
[1] 2

[[4]][[1]]$xlim
[1] 1978 2007

[[4]][[1]]$fit
               [,1]
  [1,] -23.19877967
  [2,] -23.10036369
  [3,] -23.00086500
  [4,] -22.89920090
  [5,] -22.79426504
  [6,] -22.68457746
  [7,] -22.56835993
  [8,] -22.44382561
  [9,] -22.30909475
 [10,] -22.16206341
 [11,] -22.00059458
 [12,] -21.82254909
 [13,] -21.62576959
 [14,] -21.40808958
 [15,] -21.16734425
 [16,] -20.90146366
 [17,] -20.60852057
 [18,] -20.28659951
 [19,] -19.93385001
 [20,] -19.54874164
 [21,] -19.12984225
 [22,] -18.67573494
 [23,] -18.18532628
 [24,] -17.65783206
 [25,] -17.09248059
 [26,] -16.48867355
 [27,] -15.84632254
 [28,] -15.16543244
 [29,] -14.44605351
 [30,] -13.68872171
 [31,] -12.89426765
 [32,] -12.06352893
 [33,] -11.19761545
 [34,] -10.29812981
 [35,]  -9.36672651
 [36,]  -8.40514008
 [37,]  -7.41559144
 [38,]  -6.40048429
 [39,]  -5.36223203
 [40,]  -4.30352708
 [41,]  -3.22738122
 [42,]  -2.13682371
 [43,]  -1.03496792
 [44,]   0.07476943
 [45,]   1.18890326
 [46,]   2.30393841
 [47,]   3.41624081
 [48,]   4.52207515
 [49,]   5.61770376
 [50,]   6.69938080
 [51,]   7.76334253
 [52,]   8.80582283
 [53,]   9.82307237
 [54,]  10.81146865
 [55,]  11.76744713
 [56,]  12.68744745
 [57,]  13.56807913
 [58,]  14.40618485
 [59,]  15.19862416
 [60,]  15.94235001
 [61,]  16.63472969
 [62,]  17.27324538
 [63,]  17.85540121
 [64,]  18.37910212
 [65,]  18.84260326
 [66,]  19.24417194
 [67,]  19.58229447
 [68,]  19.85604008
 [69,]  20.06457387
 [70,]  20.20712129
 [71,]  20.28348065
 [72,]  20.29376688
 [73,]  20.23810290
 [74,]  20.11694623
 [75,]  19.93130587
 [76,]  19.68224237
 [77,]  19.37091969
 [78,]  18.99906722
 [79,]  18.56860654
 [80,]  18.08147267
 [81,]  17.53993234
 [82,]  16.94659921
 [83,]  16.30410332
 [84,]  15.61517320
 [85,]  14.88285814
 [86,]  14.11027257
 [87,]  13.30053996
 [88,]  12.45689347
 [89,]  11.58263923
 [90,]  10.68108430
 [91,]   9.75548591
 [92,]   8.80900217
 [93,]   7.84477947
 [94,]   6.86591019
 [95,]   5.87512104
 [96,]   4.87498705
 [97,]   3.86807059
 [98,]   2.85649611
 [99,]   1.84183940
[100,]   0.82564158

[[4]][[1]]$plot.me
[1] TRUE



[[5]]
[[5]][[1]]
[[5]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[5]][[1]]$scale
[1] TRUE

[[5]][[1]]$se
  [1] 4.15484109 4.07090491 3.98696873 3.90303254 3.81909636 3.73516018
  [7] 3.65122399 3.56728781 3.48335163 3.39941544 3.31547926 3.23154307
 [13] 3.14760689 3.06367071 2.97973452 2.89579834 2.81186216 2.72792597
 [19] 2.64398979 2.56005360 2.47611742 2.39218124 2.30824505 2.22430887
 [25] 2.14037269 2.05643650 1.97250032 1.88856413 1.80462795 1.72069177
 [31] 1.63675558 1.55281940 1.46888322 1.38494703 1.30101085 1.21707466
 [37] 1.13313848 1.04920230 0.96526611 0.88132993 0.79739375 0.71345756
 [43] 0.62952138 0.54558519 0.46164901 0.37771283 0.29377664 0.20984046
 [49] 0.12590428 0.04196809 0.04196809 0.12590428 0.20984046 0.29377664
 [55] 0.37771283 0.46164901 0.54558519 0.62952138 0.71345756 0.79739375
 [61] 0.88132993 0.96526611 1.04920230 1.13313848 1.21707466 1.30101085
 [67] 1.38494703 1.46888322 1.55281940 1.63675558 1.72069177 1.80462795
 [73] 1.88856413 1.97250032 2.05643650 2.14037269 2.22430887 2.30824505
 [79] 2.39218124 2.47611742 2.56005360 2.64398979 2.72792597 2.81186216
 [85] 2.89579834 2.97973452 3.06367071 3.14760689 3.23154307 3.31547926
 [91] 3.39941544 3.48335163 3.56728781 3.65122399 3.73516018 3.81909636
 [97] 3.90303254 3.98696873 4.07090491 4.15484109

[[5]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[5]][[1]]$xlab
[1] "YEAR"

[[5]][[1]]$ylab
[1] "s(YEAR,1)"

[[5]][[1]]$main
NULL

[[5]][[1]]$se.mult
[1] 2

[[5]][[1]]$xlim
[1] 1978 2007

[[5]][[1]]$fit
              [,1]
  [1,] -3.96129032
  [2,] -3.88126426
  [3,] -3.80123819
  [4,] -3.72121212
  [5,] -3.64118605
  [6,] -3.56115999
  [7,] -3.48113392
  [8,] -3.40110785
  [9,] -3.32108179
 [10,] -3.24105572
 [11,] -3.16102965
 [12,] -3.08100358
 [13,] -3.00097752
 [14,] -2.92095145
 [15,] -2.84092538
 [16,] -2.76089932
 [17,] -2.68087325
 [18,] -2.60084718
 [19,] -2.52082111
 [20,] -2.44079505
 [21,] -2.36076898
 [22,] -2.28074291
 [23,] -2.20071685
 [24,] -2.12069078
 [25,] -2.04066471
 [26,] -1.96063864
 [27,] -1.88061258
 [28,] -1.80058651
 [29,] -1.72056044
 [30,] -1.64053438
 [31,] -1.56050831
 [32,] -1.48048224
 [33,] -1.40045617
 [34,] -1.32043011
 [35,] -1.24040404
 [36,] -1.16037797
 [37,] -1.08035191
 [38,] -1.00032584
 [39,] -0.92029977
 [40,] -0.84027370
 [41,] -0.76024764
 [42,] -0.68022157
 [43,] -0.60019550
 [44,] -0.52016944
 [45,] -0.44014337
 [46,] -0.36011730
 [47,] -0.28009123
 [48,] -0.20006517
 [49,] -0.12003910
 [50,] -0.04001303
 [51,]  0.04001303
 [52,]  0.12003910
 [53,]  0.20006517
 [54,]  0.28009123
 [55,]  0.36011730
 [56,]  0.44014337
 [57,]  0.52016944
 [58,]  0.60019550
 [59,]  0.68022157
 [60,]  0.76024764
 [61,]  0.84027370
 [62,]  0.92029977
 [63,]  1.00032584
 [64,]  1.08035191
 [65,]  1.16037797
 [66,]  1.24040404
 [67,]  1.32043011
 [68,]  1.40045617
 [69,]  1.48048224
 [70,]  1.56050831
 [71,]  1.64053438
 [72,]  1.72056044
 [73,]  1.80058651
 [74,]  1.88061258
 [75,]  1.96063864
 [76,]  2.04066471
 [77,]  2.12069078
 [78,]  2.20071685
 [79,]  2.28074291
 [80,]  2.36076898
 [81,]  2.44079505
 [82,]  2.52082111
 [83,]  2.60084718
 [84,]  2.68087325
 [85,]  2.76089932
 [86,]  2.84092538
 [87,]  2.92095145
 [88,]  3.00097752
 [89,]  3.08100358
 [90,]  3.16102965
 [91,]  3.24105572
 [92,]  3.32108179
 [93,]  3.40110785
 [94,]  3.48113392
 [95,]  3.56115999
 [96,]  3.64118605
 [97,]  3.72121212
 [98,]  3.80123819
 [99,]  3.88126426
[100,]  3.96129032

[[5]][[1]]$plot.me
[1] TRUE



[[6]]
[[6]][[1]]
[[6]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[6]][[1]]$scale
[1] TRUE

[[6]][[1]]$se
  [1] 4.5749248 4.4822190 4.3895250 4.2968438 4.2041763 4.1115235 4.0188866
  [8] 3.9262666 3.8336644 3.7410812 3.6485177 3.5559750 3.4634538 3.3709549
 [15] 3.2784789 3.1860263 3.0935977 3.0011934 2.9088137 2.8164588 2.7241289
 [22] 2.6318241 2.5395446 2.4472903 2.3550615 2.2628583 2.1706810 2.0785301
 [29] 1.9864063 1.8943106 1.8022444 1.7102096 1.6182088 1.5262455 1.4343246
 [36] 1.3424521 1.2506368 1.1588900 1.0672277 0.9756718 0.8842541 0.7930208
 [43] 0.7020426 0.6114326 0.5213817 0.4322389 0.3447087 0.2604218 0.1838927
 [50] 0.1296727 0.1296727 0.1838927 0.2604218 0.3447087 0.4322389 0.5213817
 [57] 0.6114326 0.7020426 0.7930208 0.8842541 0.9756718 1.0672277 1.1588900
 [64] 1.2506368 1.3424521 1.4343246 1.5262455 1.6182088 1.7102096 1.8022444
 [71] 1.8943106 1.9864063 2.0785301 2.1706810 2.2628583 2.3550615 2.4472903
 [78] 2.5395446 2.6318241 2.7241289 2.8164588 2.9088137 3.0011934 3.0935977
 [85] 3.1860263 3.2784789 3.3709549 3.4634538 3.5559750 3.6485177 3.7410812
 [92] 3.8336644 3.9262666 4.0188866 4.1115235 4.2041763 4.2968438 4.3895250
 [99] 4.4822190 4.5749248

[[6]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[6]][[1]]$xlab
[1] "YEAR"

[[6]][[1]]$ylab
[1] "s(YEAR,1)"

[[6]][[1]]$main
NULL

[[6]][[1]]$se.mult
[1] 2

[[6]][[1]]$xlim
[1] 1978 2007

[[6]][[1]]$fit
              [,1]
  [1,] -3.35532657
  [2,] -3.28743071
  [3,] -3.21953493
  [4,] -3.15163932
  [5,] -3.08374394
  [6,] -3.01584892
  [7,] -2.94795439
  [8,] -2.88006049
  [9,] -2.81216737
 [10,] -2.74427520
 [11,] -2.67638416
 [12,] -2.60849442
 [13,] -2.54060617
 [14,] -2.47271961
 [15,] -2.40483495
 [16,] -2.33695237
 [17,] -2.26907209
 [18,] -2.20119431
 [19,] -2.13331924
 [20,] -2.06544709
 [21,] -1.99757805
 [22,] -1.92971233
 [23,] -1.86185014
 [24,] -1.79399166
 [25,] -1.72613709
 [26,] -1.65828662
 [27,] -1.59044043
 [28,] -1.52259870
 [29,] -1.45476159
 [30,] -1.38692928
 [31,] -1.31910192
 [32,] -1.25127967
 [33,] -1.18346267
 [34,] -1.11565105
 [35,] -1.04784494
 [36,] -0.98004447
 [37,] -0.91224975
 [38,] -0.84446089
 [39,] -0.77667797
 [40,] -0.70890110
 [41,] -0.64113035
 [42,] -0.57336579
 [43,] -0.50560748
 [44,] -0.43785549
 [45,] -0.37010984
 [46,] -0.30237059
 [47,] -0.23463776
 [48,] -0.16691136
 [49,] -0.09919142
 [50,] -0.03147794
 [51,]  0.03622911
 [52,]  0.10392972
 [53,]  0.17162391
 [54,]  0.23931172
 [55,]  0.30699320
 [56,]  0.37466838
 [57,]  0.44233732
 [58,]  0.51000008
 [59,]  0.57765674
 [60,]  0.64530736
 [61,]  0.71295204
 [62,]  0.78059088
 [63,]  0.84822396
 [64,]  0.91585139
 [65,]  0.98347330
 [66,]  1.05108979
 [67,]  1.11870100
 [68,]  1.18630706
 [69,]  1.25390810
 [70,]  1.32150428
 [71,]  1.38909574
 [72,]  1.45668263
 [73,]  1.52426513
 [74,]  1.59184338
 [75,]  1.65941757
 [76,]  1.72698786
 [77,]  1.79455443
 [78,]  1.86211746
 [79,]  1.92967714
 [80,]  1.99723365
 [81,]  2.06478717
 [82,]  2.13233790
 [83,]  2.19988601
 [84,]  2.26743172
 [85,]  2.33497519
 [86,]  2.40251662
 [87,]  2.47005619
 [88,]  2.53759409
 [89,]  2.60513049
 [90,]  2.67266557
 [91,]  2.74019950
 [92,]  2.80773244
 [93,]  2.87526454
 [94,]  2.94279596
 [95,]  3.01032682
 [96,]  3.07785725
 [97,]  3.14538737
 [98,]  3.21291728
 [99,]  3.28044704
[100,]  3.34797674

[[6]][[1]]$plot.me
[1] TRUE



[[7]]
[[7]][[1]]
[[7]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[7]][[1]]$scale
[1] TRUE

[[7]][[1]]$se
  [1] 4.113374 3.986321 3.860740 3.736810 3.614718 3.494672 3.376893 3.261609
  [9] 3.149050 3.039450 2.933043 2.830051 2.730688 2.635155 2.543629 2.456267
 [17] 2.373195 2.294509 2.220267 2.150490 2.085159 2.024212 1.967547 1.915027
 [25] 1.866475 1.821682 1.780423 1.742449 1.707497 1.675306 1.645624 1.618199
 [33] 1.592799 1.569224 1.547294 1.526848 1.507772 1.489980 1.473406 1.458018
 [41] 1.443818 1.430820 1.419055 1.408575 1.399440 1.391705 1.385431 1.380675
 [49] 1.377478 1.375870 1.375870 1.377478 1.380675 1.385431 1.391705 1.399440
 [57] 1.408575 1.419055 1.430820 1.443818 1.458018 1.473406 1.489980 1.507772
 [65] 1.526848 1.547294 1.569224 1.592799 1.618199 1.645624 1.675306 1.707497
 [73] 1.742449 1.780423 1.821682 1.866475 1.915027 1.967547 2.024212 2.085159
 [81] 2.150490 2.220267 2.294509 2.373195 2.456267 2.543629 2.635155 2.730688
 [89] 2.830051 2.933043 3.039450 3.149050 3.261609 3.376893 3.494672 3.614718
 [97] 3.736810 3.860740 3.986321 4.113374

[[7]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[7]][[1]]$xlab
[1] "YEAR"

[[7]][[1]]$ylab
[1] "s(YEAR,1.37)"

[[7]][[1]]$main
NULL

[[7]][[1]]$se.mult
[1] 2

[[7]][[1]]$xlim
[1] 1978 2007

[[7]][[1]]$fit
              [,1]
  [1,] -4.72624125
  [2,] -4.60219429
  [3,] -4.47817642
  [4,] -4.35421673
  [5,] -4.23034499
  [6,] -4.10660161
  [7,] -3.98303553
  [8,] -3.85969592
  [9,] -3.73663516
 [10,] -3.61391338
 [11,] -3.49159185
 [12,] -3.36973221
 [13,] -3.24839929
 [14,] -3.12765951
 [15,] -3.00757931
 [16,] -2.88822487
 [17,] -2.76966197
 [18,] -2.65195634
 [19,] -2.53517300
 [20,] -2.41937331
 [21,] -2.30461752
 [22,] -2.19096568
 [23,] -2.07847331
 [24,] -1.96719161
 [25,] -1.85717161
 [26,] -1.74846171
 [27,] -1.64110247
 [28,] -1.53513308
 [29,] -1.43059193
 [30,] -1.32750956
 [31,] -1.22591169
 [32,] -1.12582392
 [33,] -1.02726716
 [34,] -0.93025380
 [35,] -0.83479533
 [36,] -0.74090177
 [37,] -0.64857409
 [38,] -0.55780985
 [39,] -0.46860643
 [40,] -0.38095544
 [41,] -0.29484187
 [42,] -0.21025037
 [43,] -0.12716350
 [44,] -0.04555630
 [45,]  0.03459787
 [46,]  0.11332601
 [47,]  0.19066018
 [48,]  0.26663607
 [49,]  0.34128950
 [50,]  0.41465820
 [51,]  0.48678411
 [52,]  0.55770973
 [53,]  0.62747790
 [54,]  0.69613403
 [55,]  0.76372474
 [56,]  0.83029662
 [57,]  0.89589691
 [58,]  0.96057367
 [59,]  1.02437503
 [60,]  1.08734897
 [61,]  1.14954290
 [62,]  1.21100406
 [63,]  1.27177959
 [64,]  1.33191513
 [65,]  1.39145497
 [66,]  1.45044337
 [67,]  1.50892343
 [68,]  1.56693525
 [69,]  1.62451841
 [70,]  1.68171213
 [71,]  1.73855212
 [72,]  1.79507213
 [73,]  1.85130588
 [74,]  1.90728477
 [75,]  1.96303640
 [76,]  2.01858802
 [77,]  2.07396608
 [78,]  2.12919270
 [79,]  2.18428851
 [80,]  2.23927404
 [81,]  2.29416689
 [82,]  2.34898163
 [83,]  2.40373265
 [84,]  2.45843326
 [85,]  2.51309319
 [86,]  2.56772142
 [87,]  2.62232672
 [88,]  2.67691543
 [89,]  2.73149225
 [90,]  2.78606183
 [91,]  2.84062791
 [92,]  2.89519234
 [93,]  2.94975679
 [94,]  3.00432272
 [95,]  3.05889055
 [96,]  3.11346022
 [97,]  3.16803169
 [98,]  3.22260469
 [99,]  3.27717874
[100,]  3.33175330

[[7]][[1]]$plot.me
[1] TRUE



[[8]]
[[8]][[1]]
[[8]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[8]][[1]]$scale
[1] TRUE

[[8]][[1]]$se
  [1] 5.42431599 5.31473385 5.20515171 5.09556957 4.98598743 4.87640529
  [7] 4.76682315 4.65724101 4.54765886 4.43807672 4.32849458 4.21891244
 [13] 4.10933030 3.99974816 3.89016602 3.78058387 3.67100173 3.56141959
 [19] 3.45183745 3.34225531 3.23267317 3.12309103 3.01350889 2.90392674
 [25] 2.79434460 2.68476246 2.57518032 2.46559818 2.35601604 2.24643390
 [31] 2.13685176 2.02726961 1.91768747 1.80810533 1.69852319 1.58894105
 [37] 1.47935891 1.36977677 1.26019463 1.15061248 1.04103034 0.93144820
 [43] 0.82186606 0.71228392 0.60270178 0.49311964 0.38353750 0.27395535
 [49] 0.16437321 0.05479108 0.05479108 0.16437321 0.27395535 0.38353750
 [55] 0.49311964 0.60270178 0.71228392 0.82186606 0.93144820 1.04103034
 [61] 1.15061248 1.26019463 1.36977677 1.47935891 1.58894105 1.69852319
 [67] 1.80810533 1.91768747 2.02726961 2.13685176 2.24643390 2.35601604
 [73] 2.46559818 2.57518032 2.68476246 2.79434460 2.90392674 3.01350889
 [79] 3.12309103 3.23267317 3.34225531 3.45183745 3.56141959 3.67100173
 [85] 3.78058387 3.89016602 3.99974816 4.10933030 4.21891244 4.32849458
 [91] 4.43807672 4.54765886 4.65724101 4.76682315 4.87640529 4.98598743
 [97] 5.09556957 5.20515171 5.31473385 5.42431599

[[8]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[8]][[1]]$xlab
[1] "YEAR"

[[8]][[1]]$ylab
[1] "s(YEAR,1)"

[[8]][[1]]$main
NULL

[[8]][[1]]$se.mult
[1] 2

[[8]][[1]]$xlim
[1] 1978 2007

[[8]][[1]]$fit
              [,1]
  [1,] -3.11612903
  [2,] -3.05317693
  [3,] -2.99022483
  [4,] -2.92727273
  [5,] -2.86432063
  [6,] -2.80136852
  [7,] -2.73841642
  [8,] -2.67546432
  [9,] -2.61251222
 [10,] -2.54956012
 [11,] -2.48660802
 [12,] -2.42365591
 [13,] -2.36070381
 [14,] -2.29775171
 [15,] -2.23479961
 [16,] -2.17184751
 [17,] -2.10889541
 [18,] -2.04594330
 [19,] -1.98299120
 [20,] -1.92003910
 [21,] -1.85708700
 [22,] -1.79413490
 [23,] -1.73118280
 [24,] -1.66823069
 [25,] -1.60527859
 [26,] -1.54232649
 [27,] -1.47937439
 [28,] -1.41642229
 [29,] -1.35347019
 [30,] -1.29051808
 [31,] -1.22756598
 [32,] -1.16461388
 [33,] -1.10166178
 [34,] -1.03870968
 [35,] -0.97575758
 [36,] -0.91280547
 [37,] -0.84985337
 [38,] -0.78690127
 [39,] -0.72394917
 [40,] -0.66099707
 [41,] -0.59804497
 [42,] -0.53509286
 [43,] -0.47214076
 [44,] -0.40918866
 [45,] -0.34623656
 [46,] -0.28328446
 [47,] -0.22033236
 [48,] -0.15738025
 [49,] -0.09442815
 [50,] -0.03147605
 [51,]  0.03147605
 [52,]  0.09442815
 [53,]  0.15738025
 [54,]  0.22033236
 [55,]  0.28328446
 [56,]  0.34623656
 [57,]  0.40918866
 [58,]  0.47214076
 [59,]  0.53509286
 [60,]  0.59804497
 [61,]  0.66099707
 [62,]  0.72394917
 [63,]  0.78690127
 [64,]  0.84985337
 [65,]  0.91280547
 [66,]  0.97575758
 [67,]  1.03870968
 [68,]  1.10166178
 [69,]  1.16461388
 [70,]  1.22756598
 [71,]  1.29051808
 [72,]  1.35347019
 [73,]  1.41642229
 [74,]  1.47937439
 [75,]  1.54232649
 [76,]  1.60527859
 [77,]  1.66823069
 [78,]  1.73118280
 [79,]  1.79413490
 [80,]  1.85708700
 [81,]  1.92003910
 [82,]  1.98299120
 [83,]  2.04594330
 [84,]  2.10889541
 [85,]  2.17184751
 [86,]  2.23479961
 [87,]  2.29775171
 [88,]  2.36070381
 [89,]  2.42365591
 [90,]  2.48660802
 [91,]  2.54956012
 [92,]  2.61251222
 [93,]  2.67546432
 [94,]  2.73841642
 [95,]  2.80136852
 [96,]  2.86432063
 [97,]  2.92727273
 [98,]  2.99022483
 [99,]  3.05317693
[100,]  3.11612903

[[8]][[1]]$plot.me
[1] TRUE



[[9]]
[[9]][[1]]
[[9]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[9]][[1]]$scale
[1] TRUE

[[9]][[1]]$se
  [1] 4.3272802 4.2398604 4.1524406 4.0650208 3.9776010 3.8901812 3.8027613
  [8] 3.7153415 3.6279217 3.5405019 3.4530821 3.3656623 3.2782425 3.1908227
 [15] 3.1034029 3.0159831 2.9285633 2.8411435 2.7537237 2.6663039 2.5788841
 [22] 2.4914643 2.4040445 2.3166247 2.2292049 2.1417851 2.0543653 1.9669455
 [29] 1.8795257 1.7921059 1.7046861 1.6172663 1.5298465 1.4424267 1.3550069
 [36] 1.2675871 1.1801673 1.0927475 1.0053277 0.9179079 0.8304881 0.7430683
 [43] 0.6556485 0.5682287 0.4808089 0.3933891 0.3059693 0.2185495 0.1311297
 [50] 0.0437099 0.0437099 0.1311297 0.2185495 0.3059693 0.3933891 0.4808089
 [57] 0.5682287 0.6556485 0.7430683 0.8304881 0.9179079 1.0053277 1.0927475
 [64] 1.1801673 1.2675871 1.3550069 1.4424267 1.5298465 1.6172663 1.7046861
 [71] 1.7921059 1.8795257 1.9669455 2.0543653 2.1417851 2.2292049 2.3166247
 [78] 2.4040445 2.4914643 2.5788841 2.6663039 2.7537237 2.8411435 2.9285633
 [85] 3.0159831 3.1034029 3.1908227 3.2782425 3.3656623 3.4530821 3.5405019
 [92] 3.6279217 3.7153415 3.8027613 3.8901812 3.9776010 4.0650208 4.1524406
 [99] 4.2398604 4.3272802

[[9]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[9]][[1]]$xlab
[1] "YEAR"

[[9]][[1]]$ylab
[1] "s(YEAR,1)"

[[9]][[1]]$main
NULL

[[9]][[1]]$se.mult
[1] 2

[[9]][[1]]$xlim
[1] 1978 2007

[[9]][[1]]$fit
              [,1]
  [1,]  7.48064516
  [2,]  7.32952102
  [3,]  7.17839687
  [4,]  7.02727273
  [5,]  6.87614858
  [6,]  6.72502444
  [7,]  6.57390029
  [8,]  6.42277615
  [9,]  6.27165200
 [10,]  6.12052786
 [11,]  5.96940371
 [12,]  5.81827957
 [13,]  5.66715543
 [14,]  5.51603128
 [15,]  5.36490714
 [16,]  5.21378299
 [17,]  5.06265885
 [18,]  4.91153470
 [19,]  4.76041056
 [20,]  4.60928641
 [21,]  4.45816227
 [22,]  4.30703812
 [23,]  4.15591398
 [24,]  4.00478983
 [25,]  3.85366569
 [26,]  3.70254154
 [27,]  3.55141740
 [28,]  3.40029326
 [29,]  3.24916911
 [30,]  3.09804497
 [31,]  2.94692082
 [32,]  2.79579668
 [33,]  2.64467253
 [34,]  2.49354839
 [35,]  2.34242424
 [36,]  2.19130010
 [37,]  2.04017595
 [38,]  1.88905181
 [39,]  1.73792766
 [40,]  1.58680352
 [41,]  1.43567937
 [42,]  1.28455523
 [43,]  1.13343109
 [44,]  0.98230694
 [45,]  0.83118280
 [46,]  0.68005865
 [47,]  0.52893451
 [48,]  0.37781036
 [49,]  0.22668622
 [50,]  0.07556207
 [51,] -0.07556207
 [52,] -0.22668622
 [53,] -0.37781036
 [54,] -0.52893451
 [55,] -0.68005865
 [56,] -0.83118280
 [57,] -0.98230694
 [58,] -1.13343109
 [59,] -1.28455523
 [60,] -1.43567937
 [61,] -1.58680352
 [62,] -1.73792766
 [63,] -1.88905181
 [64,] -2.04017595
 [65,] -2.19130010
 [66,] -2.34242424
 [67,] -2.49354839
 [68,] -2.64467253
 [69,] -2.79579668
 [70,] -2.94692082
 [71,] -3.09804497
 [72,] -3.24916911
 [73,] -3.40029326
 [74,] -3.55141740
 [75,] -3.70254154
 [76,] -3.85366569
 [77,] -4.00478983
 [78,] -4.15591398
 [79,] -4.30703812
 [80,] -4.45816227
 [81,] -4.60928641
 [82,] -4.76041056
 [83,] -4.91153470
 [84,] -5.06265885
 [85,] -5.21378299
 [86,] -5.36490714
 [87,] -5.51603128
 [88,] -5.66715543
 [89,] -5.81827957
 [90,] -5.96940371
 [91,] -6.12052786
 [92,] -6.27165200
 [93,] -6.42277615
 [94,] -6.57390029
 [95,] -6.72502444
 [96,] -6.87614858
 [97,] -7.02727273
 [98,] -7.17839687
 [99,] -7.32952102
[100,] -7.48064516

[[9]][[1]]$plot.me
[1] TRUE



[[10]]
[[10]][[1]]
[[10]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[10]][[1]]$scale
[1] TRUE

[[10]][[1]]$se
  [1] 2.75292926 2.69731452 2.64169979 2.58608506 2.53047033 2.47485559
  [7] 2.41924086 2.36362613 2.30801140 2.25239666 2.19678193 2.14116720
 [13] 2.08555247 2.02993773 1.97432300 1.91870827 1.86309354 1.80747881
 [19] 1.75186407 1.69624934 1.64063461 1.58501988 1.52940514 1.47379041
 [25] 1.41817568 1.36256095 1.30694621 1.25133148 1.19571675 1.14010202
 [31] 1.08448728 1.02887255 0.97325782 0.91764309 0.86202835 0.80641362
 [37] 0.75079889 0.69518416 0.63956942 0.58395469 0.52833996 0.47272523
 [43] 0.41711049 0.36149576 0.30588103 0.25026630 0.19465156 0.13903683
 [49] 0.08342210 0.02780737 0.02780737 0.08342210 0.13903683 0.19465156
 [55] 0.25026630 0.30588103 0.36149576 0.41711049 0.47272523 0.52833996
 [61] 0.58395469 0.63956942 0.69518416 0.75079889 0.80641362 0.86202835
 [67] 0.91764309 0.97325782 1.02887255 1.08448728 1.14010202 1.19571675
 [73] 1.25133148 1.30694621 1.36256095 1.41817568 1.47379041 1.52940514
 [79] 1.58501988 1.64063461 1.69624934 1.75186407 1.80747881 1.86309354
 [85] 1.91870827 1.97432300 2.02993773 2.08555247 2.14116720 2.19678193
 [91] 2.25239666 2.30801140 2.36362613 2.41924086 2.47485559 2.53047033
 [97] 2.58608506 2.64169979 2.69731452 2.75292926

[[10]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[10]][[1]]$xlab
[1] "YEAR"

[[10]][[1]]$ylab
[1] "s(YEAR,1)"

[[10]][[1]]$main
NULL

[[10]][[1]]$se.mult
[1] 2

[[10]][[1]]$xlim
[1] 1978 2007

[[10]][[1]]$fit
              [,1]
  [1,] -2.39032258
  [2,] -2.34203324
  [3,] -2.29374389
  [4,] -2.24545455
  [5,] -2.19716520
  [6,] -2.14887586
  [7,] -2.10058651
  [8,] -2.05229717
  [9,] -2.00400782
 [10,] -1.95571848
 [11,] -1.90742913
 [12,] -1.85913978
 [13,] -1.81085044
 [14,] -1.76256109
 [15,] -1.71427175
 [16,] -1.66598240
 [17,] -1.61769306
 [18,] -1.56940371
 [19,] -1.52111437
 [20,] -1.47282502
 [21,] -1.42453568
 [22,] -1.37624633
 [23,] -1.32795699
 [24,] -1.27966764
 [25,] -1.23137830
 [26,] -1.18308895
 [27,] -1.13479961
 [28,] -1.08651026
 [29,] -1.03822092
 [30,] -0.98993157
 [31,] -0.94164223
 [32,] -0.89335288
 [33,] -0.84506354
 [34,] -0.79677419
 [35,] -0.74848485
 [36,] -0.70019550
 [37,] -0.65190616
 [38,] -0.60361681
 [39,] -0.55532747
 [40,] -0.50703812
 [41,] -0.45874878
 [42,] -0.41045943
 [43,] -0.36217009
 [44,] -0.31388074
 [45,] -0.26559140
 [46,] -0.21730205
 [47,] -0.16901271
 [48,] -0.12072336
 [49,] -0.07243402
 [50,] -0.02414467
 [51,]  0.02414467
 [52,]  0.07243402
 [53,]  0.12072336
 [54,]  0.16901271
 [55,]  0.21730205
 [56,]  0.26559140
 [57,]  0.31388074
 [58,]  0.36217009
 [59,]  0.41045943
 [60,]  0.45874878
 [61,]  0.50703812
 [62,]  0.55532747
 [63,]  0.60361681
 [64,]  0.65190616
 [65,]  0.70019550
 [66,]  0.74848485
 [67,]  0.79677419
 [68,]  0.84506354
 [69,]  0.89335288
 [70,]  0.94164223
 [71,]  0.98993157
 [72,]  1.03822092
 [73,]  1.08651026
 [74,]  1.13479961
 [75,]  1.18308895
 [76,]  1.23137830
 [77,]  1.27966764
 [78,]  1.32795699
 [79,]  1.37624633
 [80,]  1.42453568
 [81,]  1.47282502
 [82,]  1.52111437
 [83,]  1.56940371
 [84,]  1.61769306
 [85,]  1.66598240
 [86,]  1.71427175
 [87,]  1.76256109
 [88,]  1.81085044
 [89,]  1.85913978
 [90,]  1.90742913
 [91,]  1.95571848
 [92,]  2.00400782
 [93,]  2.05229717
 [94,]  2.10058651
 [95,]  2.14887586
 [96,]  2.19716520
 [97,]  2.24545455
 [98,]  2.29374389
 [99,]  2.34203324
[100,]  2.39032258

[[10]][[1]]$plot.me
[1] TRUE



[[11]]
[[11]][[1]]
[[11]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[11]][[1]]$scale
[1] TRUE

[[11]][[1]]$se
  [1] 3.06815016 3.00616733 2.94418450 2.88220167 2.82021884 2.75823600
  [7] 2.69625317 2.63427034 2.57228751 2.51030468 2.44832185 2.38633901
 [13] 2.32435618 2.26237335 2.20039052 2.13840769 2.07642486 2.01444203
 [19] 1.95245919 1.89047636 1.82849353 1.76651070 1.70452787 1.64254504
 [25] 1.58056220 1.51857937 1.45659654 1.39461371 1.33263088 1.27064805
 [31] 1.20866522 1.14668238 1.08469955 1.02271672 0.96073389 0.89875106
 [37] 0.83676823 0.77478539 0.71280256 0.65081973 0.58883690 0.52685407
 [43] 0.46487124 0.40288841 0.34090557 0.27892274 0.21693991 0.15495708
 [49] 0.09297425 0.03099142 0.03099142 0.09297425 0.15495708 0.21693991
 [55] 0.27892274 0.34090557 0.40288841 0.46487124 0.52685407 0.58883690
 [61] 0.65081973 0.71280256 0.77478539 0.83676823 0.89875106 0.96073389
 [67] 1.02271672 1.08469955 1.14668238 1.20866522 1.27064805 1.33263088
 [73] 1.39461371 1.45659654 1.51857937 1.58056220 1.64254504 1.70452787
 [79] 1.76651070 1.82849353 1.89047636 1.95245919 2.01444203 2.07642486
 [85] 2.13840769 2.20039052 2.26237335 2.32435618 2.38633901 2.44832185
 [91] 2.51030468 2.57228751 2.63427034 2.69625317 2.75823600 2.82021884
 [97] 2.88220167 2.94418450 3.00616733 3.06815016

[[11]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[11]][[1]]$xlab
[1] "YEAR"

[[11]][[1]]$ylab
[1] "s(YEAR,1)"

[[11]][[1]]$main
NULL

[[11]][[1]]$se.mult
[1] 2

[[11]][[1]]$xlim
[1] 1978 2007

[[11]][[1]]$fit
              [,1]
  [1,] -5.77419355
  [2,] -5.65754317
  [3,] -5.54089280
  [4,] -5.42424242
  [5,] -5.30759205
  [6,] -5.19094167
  [7,] -5.07429130
  [8,] -4.95764093
  [9,] -4.84099055
 [10,] -4.72434018
 [11,] -4.60768980
 [12,] -4.49103943
 [13,] -4.37438905
 [14,] -4.25773868
 [15,] -4.14108830
 [16,] -4.02443793
 [17,] -3.90778755
 [18,] -3.79113718
 [19,] -3.67448680
 [20,] -3.55783643
 [21,] -3.44118605
 [22,] -3.32453568
 [23,] -3.20788530
 [24,] -3.09123493
 [25,] -2.97458456
 [26,] -2.85793418
 [27,] -2.74128381
 [28,] -2.62463343
 [29,] -2.50798306
 [30,] -2.39133268
 [31,] -2.27468231
 [32,] -2.15803193
 [33,] -2.04138156
 [34,] -1.92473118
 [35,] -1.80808081
 [36,] -1.69143043
 [37,] -1.57478006
 [38,] -1.45812968
 [39,] -1.34147931
 [40,] -1.22482893
 [41,] -1.10817856
 [42,] -0.99152819
 [43,] -0.87487781
 [44,] -0.75822744
 [45,] -0.64157706
 [46,] -0.52492669
 [47,] -0.40827631
 [48,] -0.29162594
 [49,] -0.17497556
 [50,] -0.05832519
 [51,]  0.05832519
 [52,]  0.17497556
 [53,]  0.29162594
 [54,]  0.40827631
 [55,]  0.52492669
 [56,]  0.64157706
 [57,]  0.75822744
 [58,]  0.87487781
 [59,]  0.99152819
 [60,]  1.10817856
 [61,]  1.22482893
 [62,]  1.34147931
 [63,]  1.45812968
 [64,]  1.57478006
 [65,]  1.69143043
 [66,]  1.80808081
 [67,]  1.92473118
 [68,]  2.04138156
 [69,]  2.15803193
 [70,]  2.27468231
 [71,]  2.39133268
 [72,]  2.50798306
 [73,]  2.62463343
 [74,]  2.74128381
 [75,]  2.85793418
 [76,]  2.97458456
 [77,]  3.09123493
 [78,]  3.20788530
 [79,]  3.32453568
 [80,]  3.44118605
 [81,]  3.55783643
 [82,]  3.67448680
 [83,]  3.79113718
 [84,]  3.90778755
 [85,]  4.02443793
 [86,]  4.14108830
 [87,]  4.25773868
 [88,]  4.37438905
 [89,]  4.49103943
 [90,]  4.60768980
 [91,]  4.72434018
 [92,]  4.84099055
 [93,]  4.95764093
 [94,]  5.07429130
 [95,]  5.19094167
 [96,]  5.30759205
 [97,]  5.42424242
 [98,]  5.54089280
 [99,]  5.65754317
[100,]  5.77419355

[[11]][[1]]$plot.me
[1] TRUE



[[12]]
[[12]][[1]]
[[12]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[12]][[1]]$scale
[1] TRUE

[[12]][[1]]$se
  [1] 4.555740 4.339754 4.127369 3.919273 3.716234 3.519151 3.329047 3.147022
  [9] 2.974268 2.812064 2.661725 2.524553 2.401785 2.294495 2.203490 2.129204
 [17] 2.071607 2.030139 2.003708 1.990773 1.989435 1.997560 2.012957 2.033502
 [25] 2.057185 2.082185 2.106963 2.130201 2.150788 2.167884 2.180874 2.189296
 [33] 2.192878 2.191560 2.185404 2.174587 2.159467 2.140517 2.118285 2.093440
 [41] 2.066760 2.039069 2.011237 1.984192 1.958856 1.936109 1.916777 1.901588
 [49] 1.891120 1.885778 1.885778 1.891120 1.901588 1.916777 1.936109 1.958856
 [57] 1.984192 2.011237 2.039069 2.066760 2.093440 2.118285 2.140517 2.159467
 [65] 2.174587 2.185404 2.191560 2.192878 2.189296 2.180874 2.167884 2.150788
 [73] 2.130201 2.106963 2.082185 2.057185 2.033502 2.012957 1.997560 1.989435
 [81] 1.990773 2.003708 2.030139 2.071607 2.129204 2.203490 2.294495 2.401785
 [89] 2.524553 2.661725 2.812064 2.974268 3.147022 3.329047 3.519151 3.716234
 [97] 3.919273 4.127369 4.339754 4.555740

[[12]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[12]][[1]]$xlab
[1] "YEAR"

[[12]][[1]]$ylab
[1] "s(YEAR,2.47)"

[[12]][[1]]$main
NULL

[[12]][[1]]$se.mult
[1] 2

[[12]][[1]]$xlim
[1] 1978 2007

[[12]][[1]]$fit
              [,1]
  [1,] -2.36830005
  [2,] -2.15101870
  [3,] -1.93396467
  [4,] -1.71736526
  [5,] -1.50145295
  [6,] -1.28654169
  [7,] -1.07301049
  [8,] -0.86124024
  [9,] -0.65163486
 [10,] -0.44465376
 [11,] -0.24076457
 [12,] -0.04043695
 [13,]  0.15584237
 [14,]  0.34757806
 [15,]  0.53427486
 [16,]  0.71544620
 [17,]  0.89061852
 [18,]  1.05931934
 [19,]  1.22108486
 [20,]  1.37549402
 [21,]  1.52213894
 [22,]  1.66061392
 [23,]  1.79056063
 [24,]  1.91166600
 [25,]  2.02361879
 [26,]  2.12613426
 [27,]  2.21900567
 [28,]  2.30204052
 [29,]  2.37505350
 [30,]  2.43793589
 [31,]  2.49062548
 [32,]  2.53306115
 [33,]  2.56522612
 [34,]  2.58718374
 [35,]  2.59900580
 [36,]  2.60077764
 [37,]  2.59266689
 [38,]  2.57487207
 [39,]  2.54759346
 [40,]  2.51108138
 [41,]  2.46564349
 [42,]  2.41159057
 [43,]  2.34925017
 [44,]  2.27901040
 [45,]  2.20127298
 [46,]  2.11644223
 [47,]  2.02495804
 [48,]  1.92728624
 [49,]  1.82389329
 [50,]  1.71525578
 [51,]  1.60187242
 [52,]  1.48424486
 [53,]  1.36287512
 [54,]  1.23826806
 [55,]  1.11092987
 [56,]  0.98136650
 [57,]  0.85007371
 [58,]  0.71753329
 [59,]  0.58422603
 [60,]  0.45062480
 [61,]  0.31716742
 [62,]  0.18428195
 [63,]  0.05239439
 [64,] -0.07810794
 [65,] -0.20687142
 [66,] -0.33354361
 [67,] -0.45779470
 [68,] -0.57935501
 [69,] -0.69796473
 [70,] -0.81337061
 [71,] -0.92538114
 [72,] -1.03383895
 [73,] -1.13858757
 [74,] -1.23950783
 [75,] -1.33654211
 [76,] -1.42963855
 [77,] -1.51875720
 [78,] -1.60392337
 [79,] -1.68518458
 [80,] -1.76258994
 [81,] -1.83622869
 [82,] -1.90623202
 [83,] -1.97273309
 [84,] -2.03587817
 [85,] -2.09585608
 [86,] -2.15286432
 [87,] -2.20710208
 [88,] -2.25878916
 [89,] -2.30815902
 [90,] -2.35544542
 [91,] -2.40088281
 [92,] -2.44470715
 [93,] -2.48715456
 [94,] -2.52845775
 [95,] -2.56882639
 [96,] -2.60846059
 [97,] -2.64755949
 [98,] -2.68628925
 [99,] -2.72477466
[100,] -2.76313789

[[12]][[1]]$plot.me
[1] TRUE



[[13]]
[[13]][[1]]
[[13]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[13]][[1]]$scale
[1] TRUE

[[13]][[1]]$se
  [1] 2.800206 2.706481 2.613945 2.522754 2.433074 2.345089 2.259002 2.175018
  [9] 2.093349 2.014213 1.937828 1.864404 1.794146 1.727243 1.663867 1.604163
 [17] 1.548249 1.496209 1.448083 1.403872 1.363531 1.326964 1.294032 1.264558
 [25] 1.238322 1.215072 1.194539 1.176442 1.160486 1.146388 1.133879 1.122704
 [33] 1.112629 1.103461 1.095029 1.087189 1.079841 1.072912 1.066352 1.060141
 [41] 1.054286 1.048809 1.043743 1.039140 1.035056 1.031542 1.028655 1.026443
 [49] 1.024947 1.024190 1.024190 1.024947 1.026443 1.028655 1.031542 1.035056
 [57] 1.039140 1.043743 1.048809 1.054286 1.060141 1.066352 1.072912 1.079841
 [65] 1.087189 1.095029 1.103461 1.112629 1.122704 1.133879 1.146388 1.160486
 [73] 1.176442 1.194539 1.215072 1.238322 1.264558 1.294032 1.326964 1.363531
 [81] 1.403872 1.448083 1.496209 1.548249 1.604163 1.663867 1.727243 1.794146
 [89] 1.864404 1.937828 2.014213 2.093349 2.175018 2.259002 2.345089 2.433074
 [97] 2.522754 2.613945 2.706481 2.800206

[[13]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[13]][[1]]$xlab
[1] "YEAR"

[[13]][[1]]$ylab
[1] "s(YEAR,1.5)"

[[13]][[1]]$main
NULL

[[13]][[1]]$se.mult
[1] 2

[[13]][[1]]$xlim
[1] 1978 2007

[[13]][[1]]$fit
               [,1]
  [1,] -0.060627161
  [2,] -0.032902095
  [3,] -0.005201845
  [4,]  0.022448773
  [5,]  0.050024365
  [6,]  0.077490374
  [7,]  0.104804928
  [8,]  0.131925944
  [9,]  0.158808521
 [10,]  0.185400957
 [11,]  0.211650548
 [12,]  0.237504230
 [13,]  0.262905917
 [14,]  0.287798000
 [15,]  0.312122858
 [16,]  0.335822833
 [17,]  0.358840212
 [18,]  0.381117276
 [19,]  0.402596822
 [20,]  0.423224181
 [21,]  0.442945464
 [22,]  0.461706940
 [23,]  0.479458254
 [24,]  0.496152273
 [25,]  0.511741997
 [26,]  0.526182456
 [27,]  0.539434655
 [28,]  0.551460695
 [29,]  0.562223246
 [30,]  0.571691137
 [31,]  0.579836926
 [32,]  0.586633263
 [33,]  0.592056512
 [34,]  0.596089756
 [35,]  0.598716785
 [36,]  0.599922581
 [37,]  0.599699380
 [38,]  0.598042140
 [39,]  0.594945982
 [40,]  0.590410752
 [41,]  0.584441700
 [42,]  0.577044374
 [43,]  0.568226075
 [44,]  0.558000439
 [45,]  0.546382526
 [46,]  0.533387721
 [47,]  0.519035851
 [48,]  0.503349985
 [49,]  0.486353272
 [50,]  0.468070699
 [51,]  0.448531274
 [52,]  0.427764535
 [53,]  0.405800403
 [54,]  0.382671681
 [55,]  0.358412493
 [56,]  0.333056992
 [57,]  0.306640447
 [58,]  0.279199651
 [59,]  0.250771508
 [60,]  0.221393080
 [61,]  0.191102133
 [62,]  0.159936628
 [63,]  0.127934511
 [64,]  0.095133487
 [65,]  0.061571048
 [66,]  0.027284679
 [67,] -0.007688564
 [68,] -0.043312758
 [69,] -0.079552168
 [70,] -0.116371234
 [71,] -0.153736031
 [72,] -0.191613542
 [73,] -0.229970775
 [74,] -0.268775941
 [75,] -0.307999233
 [76,] -0.347611030
 [77,] -0.387582160
 [78,] -0.427885909
 [79,] -0.468496402
 [80,] -0.509387834
 [81,] -0.550536204
 [82,] -0.591919394
 [83,] -0.633515375
 [84,] -0.675302883
 [85,] -0.717263145
 [86,] -0.759377893
 [87,] -0.801629027
 [88,] -0.844000483
 [89,] -0.886477551
 [90,] -0.929045552
 [91,] -0.971690867
 [92,] -1.014401981
 [93,] -1.057167629
 [94,] -1.099976866
 [95,] -1.142820918
 [96,] -1.185691915
 [97,] -1.228582030
 [98,] -1.271484976
 [99,] -1.314396395
[100,] -1.357312050

[[13]][[1]]$plot.me
[1] TRUE



[[14]]
[[14]][[1]]
[[14]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[14]][[1]]$scale
[1] TRUE

[[14]][[1]]$se
  [1] 3.7393685 3.6638257 3.5882829 3.5127401 3.4371973 3.3616545 3.2861117
  [8] 3.2105689 3.1350261 3.0594833 2.9839405 2.9083977 2.8328549 2.7573121
 [15] 2.6817693 2.6062265 2.5306837 2.4551410 2.3795982 2.3040554 2.2285126
 [22] 2.1529698 2.0774270 2.0018842 1.9263414 1.8507986 1.7752558 1.6997130
 [29] 1.6241702 1.5486274 1.4730846 1.3975418 1.3219990 1.2464562 1.1709134
 [36] 1.0953706 1.0198278 0.9442850 0.8687422 0.7931994 0.7176566 0.6421138
 [43] 0.5665710 0.4910282 0.4154854 0.3399426 0.2643998 0.1888570 0.1133142
 [50] 0.0377714 0.0377714 0.1133142 0.1888570 0.2643998 0.3399426 0.4154854
 [57] 0.4910282 0.5665710 0.6421138 0.7176566 0.7931994 0.8687422 0.9442850
 [64] 1.0198278 1.0953706 1.1709134 1.2464562 1.3219990 1.3975418 1.4730846
 [71] 1.5486274 1.6241702 1.6997130 1.7752558 1.8507986 1.9263414 2.0018842
 [78] 2.0774270 2.1529698 2.2285126 2.3040554 2.3795982 2.4551410 2.5306837
 [85] 2.6062265 2.6817693 2.7573121 2.8328549 2.9083977 2.9839405 3.0594833
 [92] 3.1350261 3.2105689 3.2861117 3.3616545 3.4371973 3.5127401 3.5882829
 [99] 3.6638257 3.7393685

[[14]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[14]][[1]]$xlab
[1] "YEAR"

[[14]][[1]]$ylab
[1] "s(YEAR,1)"

[[14]][[1]]$main
NULL

[[14]][[1]]$se.mult
[1] 2

[[14]][[1]]$xlim
[1] 1978 2007

[[14]][[1]]$fit
              [,1]
  [1,]  6.63548387
  [2,]  6.50143369
  [3,]  6.36738351
  [4,]  6.23333333
  [5,]  6.09928315
  [6,]  5.96523297
  [7,]  5.83118280
  [8,]  5.69713262
  [9,]  5.56308244
 [10,]  5.42903226
 [11,]  5.29498208
 [12,]  5.16093190
 [13,]  5.02688172
 [14,]  4.89283154
 [15,]  4.75878136
 [16,]  4.62473118
 [17,]  4.49068100
 [18,]  4.35663082
 [19,]  4.22258065
 [20,]  4.08853047
 [21,]  3.95448029
 [22,]  3.82043011
 [23,]  3.68637993
 [24,]  3.55232975
 [25,]  3.41827957
 [26,]  3.28422939
 [27,]  3.15017921
 [28,]  3.01612903
 [29,]  2.88207885
 [30,]  2.74802867
 [31,]  2.61397849
 [32,]  2.47992832
 [33,]  2.34587814
 [34,]  2.21182796
 [35,]  2.07777778
 [36,]  1.94372760
 [37,]  1.80967742
 [38,]  1.67562724
 [39,]  1.54157706
 [40,]  1.40752688
 [41,]  1.27347670
 [42,]  1.13942652
 [43,]  1.00537634
 [44,]  0.87132616
 [45,]  0.73727599
 [46,]  0.60322581
 [47,]  0.46917563
 [48,]  0.33512545
 [49,]  0.20107527
 [50,]  0.06702509
 [51,] -0.06702509
 [52,] -0.20107527
 [53,] -0.33512545
 [54,] -0.46917563
 [55,] -0.60322581
 [56,] -0.73727599
 [57,] -0.87132616
 [58,] -1.00537634
 [59,] -1.13942652
 [60,] -1.27347670
 [61,] -1.40752688
 [62,] -1.54157706
 [63,] -1.67562724
 [64,] -1.80967742
 [65,] -1.94372760
 [66,] -2.07777778
 [67,] -2.21182796
 [68,] -2.34587814
 [69,] -2.47992832
 [70,] -2.61397849
 [71,] -2.74802867
 [72,] -2.88207885
 [73,] -3.01612903
 [74,] -3.15017921
 [75,] -3.28422939
 [76,] -3.41827957
 [77,] -3.55232975
 [78,] -3.68637993
 [79,] -3.82043011
 [80,] -3.95448029
 [81,] -4.08853047
 [82,] -4.22258065
 [83,] -4.35663082
 [84,] -4.49068100
 [85,] -4.62473118
 [86,] -4.75878136
 [87,] -4.89283154
 [88,] -5.02688172
 [89,] -5.16093190
 [90,] -5.29498208
 [91,] -5.42903226
 [92,] -5.56308244
 [93,] -5.69713262
 [94,] -5.83118280
 [95,] -5.96523297
 [96,] -6.09928315
 [97,] -6.23333333
 [98,] -6.36738351
 [99,] -6.50143369
[100,] -6.63548387

[[14]][[1]]$plot.me
[1] TRUE



[[15]]
[[15]][[1]]
[[15]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[15]][[1]]$scale
[1] TRUE

[[15]][[1]]$se
  [1] 9.9056269 9.7055133 9.5053996 9.3052859 9.1051722 8.9050586 8.7049449
  [8] 8.5048312 8.3047175 8.1046039 7.9044902 7.7043765 7.5042628 7.3041492
 [15] 7.1040355 6.9039218 6.7038081 6.5036945 6.3035808 6.1034671 5.9033534
 [22] 5.7032397 5.5031261 5.3030124 5.1028987 4.9027850 4.7026714 4.5025577
 [29] 4.3024440 4.1023303 3.9022167 3.7021030 3.5019893 3.3018756 3.1017620
 [36] 2.9016483 2.7015346 2.5014209 2.3013073 2.1011936 1.9010799 1.7009662
 [43] 1.5008526 1.3007389 1.1006252 0.9005115 0.7003979 0.5002842 0.3001705
 [50] 0.1000568 0.1000568 0.3001705 0.5002842 0.7003979 0.9005115 1.1006252
 [57] 1.3007389 1.5008526 1.7009662 1.9010799 2.1011936 2.3013073 2.5014209
 [64] 2.7015346 2.9016483 3.1017620 3.3018756 3.5019893 3.7021030 3.9022167
 [71] 4.1023303 4.3024440 4.5025577 4.7026714 4.9027850 5.1028987 5.3030124
 [78] 5.5031261 5.7032397 5.9033534 6.1034671 6.3035808 6.5036945 6.7038081
 [85] 6.9039218 7.1040355 7.3041492 7.5042628 7.7043765 7.9044902 8.1046039
 [92] 8.3047175 8.5048312 8.7049449 8.9050586 9.1051722 9.3052859 9.5053996
 [99] 9.7055133 9.9056269

[[15]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[15]][[1]]$xlab
[1] "YEAR"

[[15]][[1]]$ylab
[1] "s(YEAR,1)"

[[15]][[1]]$main
NULL

[[15]][[1]]$se.mult
[1] 2

[[15]][[1]]$xlim
[1] 1978 2007

[[15]][[1]]$fit
              [,1]
  [1,] -4.26129032
  [2,] -4.17520365
  [3,] -4.08911698
  [4,] -4.00303030
  [5,] -3.91694363
  [6,] -3.83085696
  [7,] -3.74477028
  [8,] -3.65868361
  [9,] -3.57259694
 [10,] -3.48651026
 [11,] -3.40042359
 [12,] -3.31433692
 [13,] -3.22825024
 [14,] -3.14216357
 [15,] -3.05607690
 [16,] -2.96999022
 [17,] -2.88390355
 [18,] -2.79781688
 [19,] -2.71173021
 [20,] -2.62564353
 [21,] -2.53955686
 [22,] -2.45347019
 [23,] -2.36738351
 [24,] -2.28129684
 [25,] -2.19521017
 [26,] -2.10912349
 [27,] -2.02303682
 [28,] -1.93695015
 [29,] -1.85086347
 [30,] -1.76477680
 [31,] -1.67869013
 [32,] -1.59260345
 [33,] -1.50651678
 [34,] -1.42043011
 [35,] -1.33434343
 [36,] -1.24825676
 [37,] -1.16217009
 [38,] -1.07608341
 [39,] -0.98999674
 [40,] -0.90391007
 [41,] -0.81782340
 [42,] -0.73173672
 [43,] -0.64565005
 [44,] -0.55956338
 [45,] -0.47347670
 [46,] -0.38739003
 [47,] -0.30130336
 [48,] -0.21521668
 [49,] -0.12913001
 [50,] -0.04304334
 [51,]  0.04304334
 [52,]  0.12913001
 [53,]  0.21521668
 [54,]  0.30130336
 [55,]  0.38739003
 [56,]  0.47347670
 [57,]  0.55956338
 [58,]  0.64565005
 [59,]  0.73173672
 [60,]  0.81782340
 [61,]  0.90391007
 [62,]  0.98999674
 [63,]  1.07608341
 [64,]  1.16217009
 [65,]  1.24825676
 [66,]  1.33434343
 [67,]  1.42043011
 [68,]  1.50651678
 [69,]  1.59260345
 [70,]  1.67869013
 [71,]  1.76477680
 [72,]  1.85086347
 [73,]  1.93695015
 [74,]  2.02303682
 [75,]  2.10912349
 [76,]  2.19521017
 [77,]  2.28129684
 [78,]  2.36738351
 [79,]  2.45347019
 [80,]  2.53955686
 [81,]  2.62564353
 [82,]  2.71173021
 [83,]  2.79781688
 [84,]  2.88390355
 [85,]  2.96999022
 [86,]  3.05607690
 [87,]  3.14216357
 [88,]  3.22825024
 [89,]  3.31433692
 [90,]  3.40042359
 [91,]  3.48651026
 [92,]  3.57259694
 [93,]  3.65868361
 [94,]  3.74477028
 [95,]  3.83085696
 [96,]  3.91694363
 [97,]  4.00303030
 [98,]  4.08911698
 [99,]  4.17520365
[100,]  4.26129032

[[15]][[1]]$plot.me
[1] TRUE



[[16]]
[[16]][[1]]
[[16]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[16]][[1]]$scale
[1] TRUE

[[16]][[1]]$se
  [1] 6.746028 6.443908 6.146648 5.855122 5.570292 5.293278 5.025339 4.767815
  [9] 4.522143 4.289853 4.072507 3.871652 3.688768 3.525179 3.381943 3.259754
 [17] 3.158840 3.078878 3.018954 2.977613 2.952913 2.942530 2.943940 2.954572
 [25] 2.971877 2.993455 3.017190 3.041205 3.063869 3.083894 3.100281 3.112245
 [33] 3.119260 3.121084 3.117648 3.109043 3.095599 3.077797 3.056219 3.031593
 [41] 3.004779 2.976687 2.948271 2.920547 2.894515 2.871109 2.851206 2.835568
 [49] 2.824791 2.819291 2.819291 2.824791 2.835568 2.851206 2.871109 2.894515
 [57] 2.920547 2.948271 2.976687 3.004779 3.031593 3.056219 3.077797 3.095599
 [65] 3.109043 3.117648 3.121084 3.119260 3.112245 3.100281 3.083894 3.063869
 [73] 3.041205 3.017190 2.993455 2.971877 2.954572 2.943940 2.942530 2.952913
 [81] 2.977613 3.018954 3.078878 3.158840 3.259754 3.381943 3.525179 3.688768
 [89] 3.871652 4.072507 4.289853 4.522143 4.767815 5.025339 5.293278 5.570292
 [97] 5.855122 6.146648 6.443908 6.746028

[[16]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[16]][[1]]$xlab
[1] "YEAR"

[[16]][[1]]$ylab
[1] "s(YEAR,2.27)"

[[16]][[1]]$main
NULL

[[16]][[1]]$se.mult
[1] 2

[[16]][[1]]$xlim
[1] 1978 2007

[[16]][[1]]$fit
                [,1]
  [1,] -16.436496520
  [2,] -15.830792431
  [3,] -15.225307100
  [4,] -14.620259285
  [5,] -14.015872936
  [6,] -13.412454098
  [7,] -12.810374346
  [8,] -12.210007166
  [9,] -11.611752428
 [10,] -11.016073622
 [11,] -10.423443637
 [12,]  -9.834339202
 [13,]  -9.249269506
 [14,]  -8.668760063
 [15,]  -8.093336605
 [16,]  -7.523530110
 [17,]  -6.959879446
 [18,]  -6.402924134
 [19,]  -5.853201318
 [20,]  -5.311236465
 [21,]  -4.777551451
 [22,]  -4.252667175
 [23,]  -3.737083779
 [24,]  -3.231281557
 [25,]  -2.735739999
 [26,]  -2.250925007
 [27,]  -1.777262510
 [28,]  -1.315171124
 [29,]  -0.865065436
 [30,]  -0.427316856
 [31,]  -0.002270609
 [32,]   0.409728735
 [33,]   0.808363716
 [34,]   1.193365943
 [35,]   1.564472188
 [36,]   1.921428314
 [37,]   2.264035437
 [38,]   2.592115433
 [39,]   2.905491492
 [40,]   3.204024717
 [41,]   3.487619615
 [42,]   3.756183069
 [43,]   4.009637052
 [44,]   4.247957978
 [45,]   4.471134531
 [46,]   4.679158437
 [47,]   4.872063400
 [48,]   5.049913726
 [49,]   5.212774518
 [50,]   5.360730734
 [51,]   5.493910789
 [52,]   5.612448851
 [53,]   5.716484154
 [54,]   5.806194233
 [55,]   5.881774124
 [56,]   5.943419429
 [57,]   5.991346687
 [58,]   6.025801166
 [59,]   6.047030214
 [60,]   6.055287687
 [61,]   6.050856312
 [62,]   6.034026819
 [63,]   6.005090911
 [64,]   5.964358035
 [65,]   5.912153137
 [66,]   5.848801699
 [67,]   5.774635650
 [68,]   5.690004076
 [69,]   5.595258888
 [70,]   5.490753165
 [71,]   5.376851089
 [72,]   5.253922977
 [73,]   5.122339262
 [74,]   4.982474153
 [75,]   4.834708078
 [76,]   4.679422048
 [77,]   4.516997376
 [78,]   4.347817041
 [79,]   4.172264585
 [80,]   3.990723431
 [81,]   3.803574017
 [82,]   3.611193653
 [83,]   3.413959505
 [84,]   3.212245312
 [85,]   3.006413670
 [86,]   2.796824908
 [87,]   2.583837965
 [88,]   2.367794900
 [89,]   2.149026544
 [90,]   1.927863418
 [91,]   1.704621818
 [92,]   1.479589759
 [93,]   1.253051910
 [94,]   1.025286648
 [95,]   0.796529737
 [96,]   0.566999272
 [97,]   0.336912197
 [98,]   0.106446152
 [99,]  -0.124270463
[100,]  -0.355112365

[[16]][[1]]$plot.me
[1] TRUE



[[17]]
[[17]][[1]]
[[17]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[17]][[1]]$scale
[1] TRUE

[[17]][[1]]$se
  [1] 2.94883411 2.88926170 2.82968930 2.77011689 2.71054449 2.65097208
  [7] 2.59139967 2.53182727 2.47225486 2.41268245 2.35311005 2.29353764
 [13] 2.23396524 2.17439283 2.11482042 2.05524802 1.99567561 1.93610320
 [19] 1.87653080 1.81695839 1.75738599 1.69781358 1.63824117 1.57866877
 [25] 1.51909636 1.45952395 1.39995155 1.34037914 1.28080674 1.22123433
 [31] 1.16166192 1.10208952 1.04251711 0.98294470 0.92337230 0.86379989
 [37] 0.80422748 0.74465508 0.68508267 0.62551027 0.56593786 0.50636545
 [43] 0.44679305 0.38722064 0.32764823 0.26807583 0.20850342 0.14893102
 [49] 0.08935861 0.02978621 0.02978621 0.08935861 0.14893102 0.20850342
 [55] 0.26807583 0.32764823 0.38722064 0.44679305 0.50636545 0.56593786
 [61] 0.62551027 0.68508267 0.74465508 0.80422748 0.86379989 0.92337230
 [67] 0.98294470 1.04251711 1.10208952 1.16166192 1.22123433 1.28080674
 [73] 1.34037914 1.39995155 1.45952395 1.51909636 1.57866877 1.63824117
 [79] 1.69781358 1.75738599 1.81695839 1.87653080 1.93610320 1.99567561
 [85] 2.05524802 2.11482042 2.17439283 2.23396524 2.29353764 2.35311005
 [91] 2.41268245 2.47225486 2.53182727 2.59139967 2.65097208 2.71054449
 [97] 2.77011689 2.82968930 2.88926170 2.94883411

[[17]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[17]][[1]]$xlab
[1] "YEAR"

[[17]][[1]]$ylab
[1] "s(YEAR,1)"

[[17]][[1]]$main
NULL

[[17]][[1]]$se.mult
[1] 2

[[17]][[1]]$xlim
[1] 1978 2007

[[17]][[1]]$fit
              [,1]
  [1,]  4.74516129
  [2,]  4.64929945
  [3,]  4.55343760
  [4,]  4.45757576
  [5,]  4.36171391
  [6,]  4.26585207
  [7,]  4.16999022
  [8,]  4.07412838
  [9,]  3.97826654
 [10,]  3.88240469
 [11,]  3.78654285
 [12,]  3.69068100
 [13,]  3.59481916
 [14,]  3.49895732
 [15,]  3.40309547
 [16,]  3.30723363
 [17,]  3.21137178
 [18,]  3.11550994
 [19,]  3.01964809
 [20,]  2.92378625
 [21,]  2.82792441
 [22,]  2.73206256
 [23,]  2.63620072
 [24,]  2.54033887
 [25,]  2.44447703
 [26,]  2.34861518
 [27,]  2.25275334
 [28,]  2.15689150
 [29,]  2.06102965
 [30,]  1.96516781
 [31,]  1.86930596
 [32,]  1.77344412
 [33,]  1.67758227
 [34,]  1.58172043
 [35,]  1.48585859
 [36,]  1.38999674
 [37,]  1.29413490
 [38,]  1.19827305
 [39,]  1.10241121
 [40,]  1.00654936
 [41,]  0.91068752
 [42,]  0.81482568
 [43,]  0.71896383
 [44,]  0.62310199
 [45,]  0.52724014
 [46,]  0.43137830
 [47,]  0.33551645
 [48,]  0.23965461
 [49,]  0.14379277
 [50,]  0.04793092
 [51,] -0.04793092
 [52,] -0.14379277
 [53,] -0.23965461
 [54,] -0.33551645
 [55,] -0.43137830
 [56,] -0.52724014
 [57,] -0.62310199
 [58,] -0.71896383
 [59,] -0.81482568
 [60,] -0.91068752
 [61,] -1.00654936
 [62,] -1.10241121
 [63,] -1.19827305
 [64,] -1.29413490
 [65,] -1.38999674
 [66,] -1.48585859
 [67,] -1.58172043
 [68,] -1.67758227
 [69,] -1.77344412
 [70,] -1.86930596
 [71,] -1.96516781
 [72,] -2.06102965
 [73,] -2.15689150
 [74,] -2.25275334
 [75,] -2.34861518
 [76,] -2.44447703
 [77,] -2.54033887
 [78,] -2.63620072
 [79,] -2.73206256
 [80,] -2.82792441
 [81,] -2.92378625
 [82,] -3.01964809
 [83,] -3.11550994
 [84,] -3.21137178
 [85,] -3.30723363
 [86,] -3.40309547
 [87,] -3.49895732
 [88,] -3.59481916
 [89,] -3.69068100
 [90,] -3.78654285
 [91,] -3.88240469
 [92,] -3.97826654
 [93,] -4.07412838
 [94,] -4.16999022
 [95,] -4.26585207
 [96,] -4.36171391
 [97,] -4.45757576
 [98,] -4.55343760
 [99,] -4.64929945
[100,] -4.74516129

[[17]][[1]]$plot.me
[1] TRUE



[[18]]
[[18]][[1]]
[[18]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[18]][[1]]$scale
[1] TRUE

[[18]][[1]]$se
  [1] 6.859260 6.634205 6.411948 6.192849 5.977289 5.765693 5.558522 5.356245
  [9] 5.159345 4.968320 4.783661 4.605846 4.435334 4.272556 4.117898 3.971690
 [17] 3.834204 3.705629 3.586070 3.475540 3.373956 3.281123 3.196756 3.120480
 [25] 3.051829 2.990262 2.935205 2.886041 2.842124 2.802830 2.767562 2.735741
 [33] 2.706840 2.680414 2.656069 2.633467 2.612367 2.592592 2.574014 2.556575
 [41] 2.540282 2.525171 2.511310 2.498809 2.487787 2.478359 2.470647 2.464761
 [49] 2.460787 2.458780 2.458780 2.460787 2.464761 2.470647 2.478359 2.487787
 [57] 2.498809 2.511310 2.525171 2.540282 2.556575 2.574014 2.592592 2.612367
 [65] 2.633467 2.656069 2.680414 2.706840 2.735741 2.767562 2.802830 2.842124
 [73] 2.886041 2.935205 2.990262 3.051829 3.120480 3.196756 3.281123 3.373956
 [81] 3.475540 3.586070 3.705629 3.834204 3.971690 4.117898 4.272556 4.435334
 [89] 4.605846 4.783661 4.968320 5.159345 5.356245 5.558522 5.765693 5.977289
 [97] 6.192849 6.411948 6.634205 6.859260

[[18]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[18]][[1]]$xlab
[1] "YEAR"

[[18]][[1]]$ylab
[1] "s(YEAR,1.47)"

[[18]][[1]]$main
NULL

[[18]][[1]]$se.mult
[1] 2

[[18]][[1]]$xlim
[1] 1978 2007

[[18]][[1]]$fit
              [,1]
  [1,] -6.09833367
  [2,] -5.91525785
  [3,] -5.73224958
  [4,] -5.54937638
  [5,] -5.36670734
  [6,] -5.18433609
  [7,] -5.00237581
  [8,] -4.82094028
  [9,] -4.64015047
 [10,] -4.46014472
 [11,] -4.28106393
 [12,] -4.10304978
 [13,] -3.92625040
 [14,] -3.75081718
 [15,] -3.57690149
 [16,] -3.40465330
 [17,] -3.23422050
 [18,] -3.06575076
 [19,] -2.89938972
 [20,] -2.73527285
 [21,] -2.57353249
 [22,] -2.41430043
 [23,] -2.25769652
 [24,] -2.10382920
 [25,] -1.95280648
 [26,] -1.80472950
 [27,] -1.65967924
 [28,] -1.51773303
 [29,] -1.37896628
 [30,] -1.24343431
 [31,] -1.11118021
 [32,] -0.98224675
 [33,] -0.85666492
 [34,] -0.73444428
 [35,] -0.61559216
 [36,] -0.50011219
 [37,] -0.38798563
 [38,] -0.27918532
 [39,] -0.17368361
 [40,] -0.07143888
 [41,]  0.02760652
 [42,]  0.12351111
 [43,]  0.21633831
 [44,]  0.30616920
 [45,]  0.39308881
 [46,]  0.47718303
 [47,]  0.55854895
 [48,]  0.63729188
 [49,]  0.71351731
 [50,]  0.78733462
 [51,]  0.85886169
 [52,]  0.92821750
 [53,]  0.99552155
 [54,]  1.06089728
 [55,]  1.12446988
 [56,]  1.18636457
 [57,]  1.24670618
 [58,]  1.30561903
 [59,]  1.36322740
 [60,]  1.41965443
 [61,]  1.47501826
 [62,]  1.52943562
 [63,]  1.58302288
 [64,]  1.63588966
 [65,]  1.68813971
 [66,]  1.73987656
 [67,]  1.79119945
 [68,]  1.84219623
 [69,]  1.89295287
 [70,]  1.94355405
 [71,]  1.99407218
 [72,]  2.04457289
 [73,]  2.09512161
 [74,]  2.14577614
 [75,]  2.19658161
 [76,]  2.24758197
 [77,]  2.29881866
 [78,]  2.35031927
 [79,]  2.40210671
 [80,]  2.45420350
 [81,]  2.50662335
 [82,]  2.55937069
 [83,]  2.61244951
 [84,]  2.66586073
 [85,]  2.71959518
 [86,]  2.77364161
 [87,]  2.82798834
 [88,]  2.88261777
 [89,]  2.93750845
 [90,]  2.99263881
 [91,]  3.04798591
 [92,]  3.10352407
 [93,]  3.15922725
 [94,]  3.21506963
 [95,]  3.27102664
 [96,]  3.32707424
 [97,]  3.38318846
 [98,]  3.43934907
 [99,]  3.49554039
[100,]  3.55174708

[[18]][[1]]$plot.me
[1] TRUE



[[19]]
[[19]][[1]]
[[19]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[19]][[1]]$scale
[1] TRUE

[[19]][[1]]$se
  [1] 5.07852944 4.97593289 4.87333633 4.77073978 4.66814322 4.56554667
  [7] 4.46295011 4.36035356 4.25775701 4.15516045 4.05256390 3.94996734
 [13] 3.84737079 3.74477423 3.64217768 3.53958113 3.43698457 3.33438802
 [19] 3.23179146 3.12919491 3.02659835 2.92400180 2.82140524 2.71880869
 [25] 2.61621214 2.51361558 2.41101903 2.30842247 2.20582592 2.10322936
 [31] 2.00063281 1.89803626 1.79543970 1.69284315 1.59024659 1.48765004
 [37] 1.38505348 1.28245693 1.17986038 1.07726382 0.97466727 0.87207071
 [43] 0.76947416 0.66687760 0.56428105 0.46168450 0.35908794 0.25649139
 [49] 0.15389483 0.05129828 0.05129828 0.15389483 0.25649139 0.35908794
 [55] 0.46168450 0.56428105 0.66687760 0.76947416 0.87207071 0.97466727
 [61] 1.07726382 1.17986038 1.28245693 1.38505348 1.48765004 1.59024659
 [67] 1.69284315 1.79543970 1.89803626 2.00063281 2.10322936 2.20582592
 [73] 2.30842247 2.41101903 2.51361558 2.61621214 2.71880869 2.82140524
 [79] 2.92400180 3.02659835 3.12919491 3.23179146 3.33438802 3.43698457
 [85] 3.53958113 3.64217768 3.74477423 3.84737079 3.94996734 4.05256390
 [91] 4.15516045 4.25775701 4.36035356 4.46295011 4.56554667 4.66814322
 [97] 4.77073978 4.87333633 4.97593289 5.07852944

[[19]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[19]][[1]]$xlab
[1] "YEAR"

[[19]][[1]]$ylab
[1] "s(YEAR,1)"

[[19]][[1]]$main
NULL

[[19]][[1]]$se.mult
[1] 2

[[19]][[1]]$xlim
[1] 1978 2007

[[19]][[1]]$fit
              [,1]
  [1,]  5.60967742
  [2,]  5.49635060
  [3,]  5.38302379
  [4,]  5.26969697
  [5,]  5.15637015
  [6,]  5.04304334
  [7,]  4.92971652
  [8,]  4.81638970
  [9,]  4.70306289
 [10,]  4.58973607
 [11,]  4.47640925
 [12,]  4.36308244
 [13,]  4.24975562
 [14,]  4.13642880
 [15,]  4.02310199
 [16,]  3.90977517
 [17,]  3.79644835
 [18,]  3.68312154
 [19,]  3.56979472
 [20,]  3.45646790
 [21,]  3.34314109
 [22,]  3.22981427
 [23,]  3.11648746
 [24,]  3.00316064
 [25,]  2.88983382
 [26,]  2.77650701
 [27,]  2.66318019
 [28,]  2.54985337
 [29,]  2.43652656
 [30,]  2.32319974
 [31,]  2.20987292
 [32,]  2.09654611
 [33,]  1.98321929
 [34,]  1.86989247
 [35,]  1.75656566
 [36,]  1.64323884
 [37,]  1.52991202
 [38,]  1.41658521
 [39,]  1.30325839
 [40,]  1.18993157
 [41,]  1.07660476
 [42,]  0.96327794
 [43,]  0.84995112
 [44,]  0.73662431
 [45,]  0.62329749
 [46,]  0.50997067
 [47,]  0.39664386
 [48,]  0.28331704
 [49,]  0.16999022
 [50,]  0.05666341
 [51,] -0.05666341
 [52,] -0.16999022
 [53,] -0.28331704
 [54,] -0.39664386
 [55,] -0.50997067
 [56,] -0.62329749
 [57,] -0.73662431
 [58,] -0.84995112
 [59,] -0.96327794
 [60,] -1.07660476
 [61,] -1.18993157
 [62,] -1.30325839
 [63,] -1.41658521
 [64,] -1.52991202
 [65,] -1.64323884
 [66,] -1.75656566
 [67,] -1.86989247
 [68,] -1.98321929
 [69,] -2.09654611
 [70,] -2.20987292
 [71,] -2.32319974
 [72,] -2.43652656
 [73,] -2.54985337
 [74,] -2.66318019
 [75,] -2.77650701
 [76,] -2.88983382
 [77,] -3.00316064
 [78,] -3.11648746
 [79,] -3.22981427
 [80,] -3.34314109
 [81,] -3.45646790
 [82,] -3.56979472
 [83,] -3.68312154
 [84,] -3.79644835
 [85,] -3.90977517
 [86,] -4.02310199
 [87,] -4.13642880
 [88,] -4.24975562
 [89,] -4.36308244
 [90,] -4.47640925
 [91,] -4.58973607
 [92,] -4.70306289
 [93,] -4.81638970
 [94,] -4.92971652
 [95,] -5.04304334
 [96,] -5.15637015
 [97,] -5.26969697
 [98,] -5.38302379
 [99,] -5.49635060
[100,] -5.60967742

[[19]][[1]]$plot.me
[1] TRUE



[[20]]
[[20]][[1]]
[[20]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[20]][[1]]$scale
[1] TRUE

[[20]][[1]]$se
  [1] 5.2583631 5.1485273 5.0388404 4.9293144 4.8199618 4.7107958 4.6018305
  [8] 4.4930793 4.3845554 4.2762721 4.1682419 4.0604762 3.9529858 3.8457804
 [15] 3.7388685 3.6322574 3.5259534 3.4199615 3.3142855 3.2089283 3.1038921
 [22] 2.9991779 2.8947869 2.7907198 2.6869778 2.5835623 2.4804766 2.3777252
 [29] 2.2753152 2.1732572 2.0715667 1.9702643 1.8693783 1.7689472 1.6690220
 [36] 1.5696692 1.4709781 1.3730668 1.2760916 1.1802630 1.0858677 0.9932986
 [43] 0.9031039 0.8160614 0.7332860 0.6563864 0.5876694 0.5303226 0.4883656
 [50] 0.4659721 0.4659721 0.4883656 0.5303226 0.5876694 0.6563864 0.7332860
 [57] 0.8160614 0.9031039 0.9932986 1.0858677 1.1802630 1.2760916 1.3730668
 [64] 1.4709781 1.5696692 1.6690220 1.7689472 1.8693783 1.9702643 2.0715667
 [71] 2.1732572 2.2753152 2.3777252 2.4804766 2.5835623 2.6869778 2.7907198
 [78] 2.8947869 2.9991779 3.1038921 3.2089283 3.3142855 3.4199615 3.5259534
 [85] 3.6322574 3.7388685 3.8457804 3.9529858 4.0604762 4.1682419 4.2762721
 [92] 4.3845554 4.4930793 4.6018305 4.7107958 4.8199618 4.9293144 5.0388404
 [99] 5.1485273 5.2583631

[[20]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[20]][[1]]$xlab
[1] "YEAR"

[[20]][[1]]$ylab
[1] "s(YEAR,1.02)"

[[20]][[1]]$main
NULL

[[20]][[1]]$se.mult
[1] 2

[[20]][[1]]$xlim
[1] 1978 2007

[[20]][[1]]$fit
              [,1]
  [1,]  8.94010031
  [2,]  8.76117354
  [3,]  8.58224519
  [4,]  8.40331372
  [5,]  8.22437751
  [6,]  8.04543437
  [7,]  7.86648168
  [8,]  7.68751676
  [9,]  7.50853678
 [10,]  7.32953849
 [11,]  7.15051853
 [12,]  6.97147358
 [13,]  6.79240007
 [14,]  6.61329437
 [15,]  6.43415284
 [16,]  6.25497184
 [17,]  6.07574770
 [18,]  5.89647679
 [19,]  5.71715548
 [20,]  5.53778031
 [21,]  5.35834787
 [22,]  5.17885476
 [23,]  4.99929779
 [24,]  4.81967397
 [25,]  4.63998031
 [26,]  4.46021397
 [27,]  4.28037247
 [28,]  4.10045339
 [29,]  3.92045436
 [30,]  3.74037339
 [31,]  3.56020874
 [32,]  3.37995865
 [33,]  3.19962160
 [34,]  3.01919651
 [35,]  2.83868233
 [36,]  2.65807809
 [37,]  2.47738327
 [38,]  2.29659751
 [39,]  2.11572050
 [40,]  1.93475219
 [41,]  1.75369289
 [42,]  1.57254291
 [43,]  1.39130268
 [44,]  1.20997305
 [45,]  1.02855494
 [46,]  0.84704927
 [47,]  0.66545729
 [48,]  0.48378041
 [49,]  0.30202007
 [50,]  0.12017783
 [51,] -0.06174452
 [52,] -0.24374513
 [53,] -0.42582214
 [54,] -0.60797350
 [55,] -0.79019707
 [56,] -0.97249073
 [57,] -1.15485226
 [58,] -1.33727935
 [59,] -1.51976970
 [60,] -1.70232097
 [61,] -1.88493080
 [62,] -2.06759679
 [63,] -2.25031655
 [64,] -2.43308772
 [65,] -2.61590792
 [66,] -2.79877479
 [67,] -2.98168598
 [68,] -3.16463923
 [69,] -3.34763226
 [70,] -3.53066283
 [71,] -3.71372878
 [72,] -3.89682802
 [73,] -4.07995843
 [74,] -4.26311799
 [75,] -4.44630481
 [76,] -4.62951698
 [77,] -4.81275263
 [78,] -4.99601006
 [79,] -5.17928759
 [80,] -5.36258357
 [81,] -5.54589644
 [82,] -5.72922478
 [83,] -5.91256715
 [84,] -6.09592217
 [85,] -6.27928863
 [86,] -6.46266532
 [87,] -6.64605107
 [88,] -6.82944481
 [89,] -7.01284558
 [90,] -7.19625242
 [91,] -7.37966441
 [92,] -7.56308081
 [93,] -7.74650085
 [94,] -7.92992382
 [95,] -8.11334912
 [96,] -8.29677623
 [97,] -8.48020463
 [98,] -8.66363389
 [99,] -8.84706372
[100,] -9.03049384

[[20]][[1]]$plot.me
[1] TRUE



[[21]]
[[21]][[1]]
[[21]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[21]][[1]]$scale
[1] TRUE

[[21]][[1]]$se
  [1] 4.341371 4.161236 3.983835 3.809621 3.639087 3.472801 3.311392 3.155523
  [9] 3.005899 2.863260 2.728359 2.601939 2.484719 2.377356 2.280411 2.194304
 [17] 2.119285 2.055386 2.002397 1.959870 1.927115 1.903227 1.887142 1.877704
 [25] 1.873690 1.873881 1.877136 1.882394 1.888685 1.895194 1.901251 1.906294
 [33] 1.909898 1.911792 1.911806 1.909858 1.905997 1.900359 1.893132 1.884582
 [41] 1.875045 1.864879 1.854464 1.844212 1.834525 1.825774 1.818309 1.812432
 [49] 1.808378 1.806306 1.806306 1.808378 1.812432 1.818309 1.825774 1.834525
 [57] 1.844212 1.854464 1.864879 1.875045 1.884582 1.893132 1.900359 1.905997
 [65] 1.909858 1.911806 1.911792 1.909898 1.906294 1.901251 1.895194 1.888685
 [73] 1.882394 1.877136 1.873881 1.873690 1.877704 1.887142 1.903227 1.927115
 [81] 1.959870 2.002397 2.055386 2.119285 2.194304 2.280411 2.377356 2.484719
 [89] 2.601939 2.728359 2.863260 3.005899 3.155523 3.311392 3.472801 3.639087
 [97] 3.809621 3.983835 4.161236 4.341371

[[21]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[21]][[1]]$xlab
[1] "YEAR"

[[21]][[1]]$ylab
[1] "s(YEAR,2.02)"

[[21]][[1]]$main
NULL

[[21]][[1]]$se.mult
[1] 2

[[21]][[1]]$xlim
[1] 1978 2007

[[21]][[1]]$fit
              [,1]
  [1,] -3.32027435
  [2,] -3.14684096
  [3,] -2.97348871
  [4,] -2.80029870
  [5,] -2.62735401
  [6,] -2.45476831
  [7,] -2.28267970
  [8,] -2.11122698
  [9,] -1.94055895
 [10,] -1.77084842
 [11,] -1.60227179
 [12,] -1.43500693
 [13,] -1.26924448
 [14,] -1.10518147
 [15,] -0.94301504
 [16,] -0.78294486
 [17,] -0.62517444
 [18,] -0.46990760
 [19,] -0.31734753
 [20,] -0.16769441
 [21,] -0.02114747
 [22,]  0.12209436
 [23,]  0.26183877
 [24,]  0.39789974
 [25,]  0.53009154
 [26,]  0.65823293
 [27,]  0.78215594
 [28,]  0.90169507
 [29,]  1.01668614
 [30,]  1.12697967
 [31,]  1.23243506
 [32,]  1.33291193
 [33,]  1.42827929
 [34,]  1.51842308
 [35,]  1.60323105
 [36,]  1.68259415
 [37,]  1.75642273
 [38,]  1.82463449
 [39,]  1.88714757
 [40,]  1.94389372
 [41,]  1.99482030
 [42,]  2.03987547
 [43,]  2.07901299
 [44,]  2.11220662
 [45,]  2.13943462
 [46,]  2.16067642
 [47,]  2.17592735
 [48,]  2.18519436
 [49,]  2.18848466
 [50,]  2.18581332
 [51,]  2.17721245
 [52,]  2.16271647
 [53,]  2.14236186
 [54,]  2.11620087
 [55,]  2.08429297
 [56,]  2.04669785
 [57,]  2.00348436
 [58,]  1.95473381
 [59,]  1.90052846
 [60,]  1.84095359
 [61,]  1.77610793
 [62,]  1.70609397
 [63,]  1.63101467
 [64,]  1.55098200
 [65,]  1.46611580
 [66,]  1.37653617
 [67,]  1.28236684
 [68,]  1.18374121
 [69,]  1.08079429
 [70,]  0.97366183
 [71,]  0.86248681
 [72,]  0.74741621
 [73,]  0.62859708
 [74,]  0.50617965
 [75,]  0.38031930
 [76,]  0.25117193
 [77,]  0.11889404
 [78,] -0.01635439
 [79,] -0.15441220
 [80,] -0.29511824
 [81,] -0.43831087
 [82,] -0.58382799
 [83,] -0.73150745
 [84,] -0.88118800
 [85,] -1.03271118
 [86,] -1.18591911
 [87,] -1.34065443
 [88,] -1.49676589
 [89,] -1.65410634
 [90,] -1.81252872
 [91,] -1.97189187
 [92,] -2.13206627
 [93,] -2.29292382
 [94,] -2.45433914
 [95,] -2.61620552
 [96,] -2.77842399
 [97,] -2.94089610
 [98,] -3.10354109
 [99,] -3.26630041
[100,] -3.42911689

[[21]][[1]]$plot.me
[1] TRUE



[[22]]
[[22]][[1]]
[[22]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[22]][[1]]$scale
[1] TRUE

[[22]][[1]]$se
  [1] 7.80651902 7.64881157 7.49110411 7.33339666 7.17568920 7.01798175
  [7] 6.86027429 6.70256684 6.54485938 6.38715193 6.22944447 6.07173702
 [13] 5.91402956 5.75632211 5.59861465 5.44090720 5.28319974 5.12549229
 [19] 4.96778483 4.81007738 4.65236992 4.49466247 4.33695501 4.17924756
 [25] 4.02154010 3.86383265 3.70612519 3.54841774 3.39071028 3.23300283
 [31] 3.07529537 2.91758792 2.75988046 2.60217301 2.44446555 2.28675810
 [37] 2.12905064 1.97134319 1.81363573 1.65592828 1.49822082 1.34051337
 [43] 1.18280591 1.02509846 0.86739100 0.70968355 0.55197609 0.39426864
 [49] 0.23656118 0.07885373 0.07885373 0.23656118 0.39426864 0.55197609
 [55] 0.70968355 0.86739100 1.02509846 1.18280591 1.34051337 1.49822082
 [61] 1.65592828 1.81363573 1.97134319 2.12905064 2.28675810 2.44446555
 [67] 2.60217301 2.75988046 2.91758792 3.07529537 3.23300283 3.39071028
 [73] 3.54841774 3.70612519 3.86383265 4.02154010 4.17924756 4.33695501
 [79] 4.49466247 4.65236992 4.81007738 4.96778483 5.12549229 5.28319974
 [85] 5.44090720 5.59861465 5.75632211 5.91402956 6.07173702 6.22944447
 [91] 6.38715193 6.54485938 6.70256684 6.86027429 7.01798175 7.17568920
 [97] 7.33339666 7.49110411 7.64881157 7.80651902

[[22]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[22]][[1]]$xlab
[1] "YEAR"

[[22]][[1]]$ylab
[1] "s(YEAR,1)"

[[22]][[1]]$main
NULL

[[22]][[1]]$se.mult
[1] 2

[[22]][[1]]$xlim
[1] 1978 2007

[[22]][[1]]$fit
              [,1]
  [1,] -7.54838710
  [2,] -7.39589443
  [3,] -7.24340176
  [4,] -7.09090909
  [5,] -6.93841642
  [6,] -6.78592375
  [7,] -6.63343109
  [8,] -6.48093842
  [9,] -6.32844575
 [10,] -6.17595308
 [11,] -6.02346041
 [12,] -5.87096774
 [13,] -5.71847507
 [14,] -5.56598240
 [15,] -5.41348974
 [16,] -5.26099707
 [17,] -5.10850440
 [18,] -4.95601173
 [19,] -4.80351906
 [20,] -4.65102639
 [21,] -4.49853372
 [22,] -4.34604106
 [23,] -4.19354839
 [24,] -4.04105572
 [25,] -3.88856305
 [26,] -3.73607038
 [27,] -3.58357771
 [28,] -3.43108504
 [29,] -3.27859238
 [30,] -3.12609971
 [31,] -2.97360704
 [32,] -2.82111437
 [33,] -2.66862170
 [34,] -2.51612903
 [35,] -2.36363636
 [36,] -2.21114370
 [37,] -2.05865103
 [38,] -1.90615836
 [39,] -1.75366569
 [40,] -1.60117302
 [41,] -1.44868035
 [42,] -1.29618768
 [43,] -1.14369501
 [44,] -0.99120235
 [45,] -0.83870968
 [46,] -0.68621701
 [47,] -0.53372434
 [48,] -0.38123167
 [49,] -0.22873900
 [50,] -0.07624633
 [51,]  0.07624633
 [52,]  0.22873900
 [53,]  0.38123167
 [54,]  0.53372434
 [55,]  0.68621701
 [56,]  0.83870968
 [57,]  0.99120235
 [58,]  1.14369501
 [59,]  1.29618768
 [60,]  1.44868035
 [61,]  1.60117302
 [62,]  1.75366569
 [63,]  1.90615836
 [64,]  2.05865103
 [65,]  2.21114370
 [66,]  2.36363636
 [67,]  2.51612903
 [68,]  2.66862170
 [69,]  2.82111437
 [70,]  2.97360704
 [71,]  3.12609971
 [72,]  3.27859238
 [73,]  3.43108504
 [74,]  3.58357771
 [75,]  3.73607038
 [76,]  3.88856305
 [77,]  4.04105572
 [78,]  4.19354839
 [79,]  4.34604106
 [80,]  4.49853372
 [81,]  4.65102639
 [82,]  4.80351906
 [83,]  4.95601173
 [84,]  5.10850440
 [85,]  5.26099707
 [86,]  5.41348974
 [87,]  5.56598240
 [88,]  5.71847507
 [89,]  5.87096774
 [90,]  6.02346041
 [91,]  6.17595308
 [92,]  6.32844575
 [93,]  6.48093842
 [94,]  6.63343109
 [95,]  6.78592375
 [96,]  6.93841642
 [97,]  7.09090909
 [98,]  7.24340176
 [99,]  7.39589443
[100,]  7.54838710

[[22]][[1]]$plot.me
[1] TRUE



[[23]]
[[23]][[1]]
[[23]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[23]][[1]]$scale
[1] TRUE

[[23]][[1]]$se
  [1] 3.115397 2.987926 2.862369 2.739037 2.618270 2.500457 2.386030 2.275443
  [9] 2.169176 2.067734 1.971629 1.881369 1.797441 1.720296 1.650319 1.587807
 [17] 1.532941 1.485765 1.446160 1.413851 1.388400 1.369219 1.355611 1.346806
 [25] 1.341982 1.340308 1.341003 1.343328 1.346605 1.350258 1.353807 1.356844
 [33] 1.359058 1.360243 1.360260 1.359037 1.356589 1.352993 1.348362 1.342863
 [41] 1.336714 1.330145 1.323404 1.316759 1.310475 1.304794 1.299945 1.296126
 [49] 1.293491 1.292144 1.292144 1.293491 1.296126 1.299945 1.304794 1.310475
 [57] 1.316759 1.323404 1.330145 1.336714 1.342863 1.348362 1.352993 1.356589
 [65] 1.359037 1.360260 1.360243 1.359058 1.356844 1.353807 1.350258 1.346605
 [73] 1.343328 1.341003 1.340308 1.341982 1.346806 1.355611 1.369219 1.388400
 [81] 1.413851 1.446160 1.485765 1.532941 1.587807 1.650319 1.720296 1.797441
 [89] 1.881369 1.971629 2.067734 2.169176 2.275443 2.386030 2.500457 2.618270
 [97] 2.739037 2.862369 2.987926 3.115397

[[23]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[23]][[1]]$xlab
[1] "YEAR"

[[23]][[1]]$ylab
[1] "s(YEAR,1.98)"

[[23]][[1]]$main
NULL

[[23]][[1]]$se.mult
[1] 2

[[23]][[1]]$xlim
[1] 1978 2007

[[23]][[1]]$fit
              [,1]
  [1,] -1.83491915
  [2,] -1.82428644
  [3,] -1.81366140
  [4,] -1.80305171
  [5,] -1.79246514
  [6,] -1.78191116
  [7,] -1.77140058
  [8,] -1.76094423
  [9,] -1.75055250
 [10,] -1.74023470
 [11,] -1.72999995
 [12,] -1.71985692
 [13,] -1.70981018
 [14,] -1.69986226
 [15,] -1.69001558
 [16,] -1.68026834
 [17,] -1.67061235
 [18,] -1.66103890
 [19,] -1.65153724
 [20,] -1.64208662
 [21,] -1.63266320
 [22,] -1.62324273
 [23,] -1.61379217
 [24,] -1.60427003
 [25,] -1.59463449
 [26,] -1.58483937
 [27,] -1.57482566
 [28,] -1.56453201
 [29,] -1.55389597
 [30,] -1.54284366
 [31,] -1.53129421
 [32,] -1.51916658
 [33,] -1.50637375
 [34,] -1.49281781
 [35,] -1.47839972
 [36,] -1.46301882
 [37,] -1.44656473
 [38,] -1.42892341
 [39,] -1.40998065
 [40,] -1.38961757
 [41,] -1.36770993
 [42,] -1.34413322
 [43,] -1.31876203
 [44,] -1.29146782
 [45,] -1.26212132
 [46,] -1.23059336
 [47,] -1.19675579
 [48,] -1.16048124
 [49,] -1.12164238
 [50,] -1.08011448
 [51,] -1.03577847
 [52,] -0.98851609
 [53,] -0.93821039
 [54,] -0.88475469
 [55,] -0.82804696
 [56,] -0.76798545
 [57,] -0.70447764
 [58,] -0.63744379
 [59,] -0.56680505
 [60,] -0.49248694
 [61,] -0.41443441
 [62,] -0.33259774
 [63,] -0.24692818
 [64,] -0.15739425
 [65,] -0.06397953
 [66,]  0.03333183
 [67,]  0.13454675
 [68,]  0.23964831
 [69,]  0.34861563
 [70,]  0.46142548
 [71,]  0.57803201
 [72,]  0.69837691
 [73,]  0.82240154
 [74,]  0.95003444
 [75,]  1.08118309
 [76,]  1.21575296
 [77,]  1.35364572
 [78,]  1.49474207
 [79,]  1.63891559
 [80,]  1.78603941
 [81,]  1.93597493
 [82,]  2.08857131
 [83,]  2.24367713
 [84,]  2.40113787
 [85,]  2.56078888
 [86,]  2.72246347
 [87,]  2.88599482
 [88,]  3.05121455
 [89,]  3.21795327
 [90,]  3.38604159
 [91,]  3.55531400
 [92,]  3.72561280
 [93,]  3.89678117
 [94,]  4.06866520
 [95,]  4.24113059
 [96,]  4.41405120
 [97,]  4.58730150
 [98,]  4.76077773
 [99,]  4.93440343
[100,]  5.10810387

[[23]][[1]]$plot.me
[1] TRUE



[[24]]
[[24]][[1]]
[[24]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[24]][[1]]$scale
[1] TRUE

[[24]][[1]]$se
  [1] 5.36077697 5.25247845 5.14417992 5.03588140 4.92758287 4.81928435
  [7] 4.71098582 4.60268730 4.49438877 4.38609025 4.27779172 4.16949320
 [13] 4.06119468 3.95289615 3.84459763 3.73629910 3.62800058 3.51970205
 [19] 3.41140353 3.30310500 3.19480648 3.08650795 2.97820943 2.86991090
 [25] 2.76161238 2.65331385 2.54501533 2.43671681 2.32841828 2.22011976
 [31] 2.11182123 2.00352271 1.89522418 1.78692566 1.67862713 1.57032861
 [37] 1.46203008 1.35373156 1.24543303 1.13713451 1.02883598 0.92053746
 [43] 0.81223894 0.70394041 0.59564189 0.48734336 0.37904484 0.27074631
 [49] 0.16244779 0.05414927 0.05414927 0.16244779 0.27074631 0.37904484
 [55] 0.48734336 0.59564189 0.70394041 0.81223894 0.92053746 1.02883598
 [61] 1.13713451 1.24543303 1.35373156 1.46203008 1.57032861 1.67862713
 [67] 1.78692566 1.89522418 2.00352271 2.11182123 2.22011976 2.32841828
 [73] 2.43671681 2.54501533 2.65331385 2.76161238 2.86991090 2.97820943
 [79] 3.08650795 3.19480648 3.30310500 3.41140353 3.51970205 3.62800058
 [85] 3.73629910 3.84459763 3.95289615 4.06119468 4.16949320 4.27779172
 [91] 4.38609025 4.49438877 4.60268730 4.71098582 4.81928435 4.92758287
 [97] 5.03588140 5.14417992 5.25247845 5.36077697

[[24]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[24]][[1]]$xlab
[1] "YEAR"

[[24]][[1]]$ylab
[1] "s(YEAR,1)"

[[24]][[1]]$main
NULL

[[24]][[1]]$se.mult
[1] 2

[[24]][[1]]$xlim
[1] 1978 2007

[[24]][[1]]$fit
              [,1]
  [1,] -5.54838710
  [2,] -5.43629847
  [3,] -5.32420984
  [4,] -5.21212121
  [5,] -5.10003258
  [6,] -4.98794396
  [7,] -4.87585533
  [8,] -4.76376670
  [9,] -4.65167807
 [10,] -4.53958944
 [11,] -4.42750081
 [12,] -4.31541219
 [13,] -4.20332356
 [14,] -4.09123493
 [15,] -3.97914630
 [16,] -3.86705767
 [17,] -3.75496905
 [18,] -3.64288042
 [19,] -3.53079179
 [20,] -3.41870316
 [21,] -3.30661453
 [22,] -3.19452590
 [23,] -3.08243728
 [24,] -2.97034865
 [25,] -2.85826002
 [26,] -2.74617139
 [27,] -2.63408276
 [28,] -2.52199413
 [29,] -2.40990551
 [30,] -2.29781688
 [31,] -2.18572825
 [32,] -2.07363962
 [33,] -1.96155099
 [34,] -1.84946237
 [35,] -1.73737374
 [36,] -1.62528511
 [37,] -1.51319648
 [38,] -1.40110785
 [39,] -1.28901922
 [40,] -1.17693060
 [41,] -1.06484197
 [42,] -0.95275334
 [43,] -0.84066471
 [44,] -0.72857608
 [45,] -0.61648746
 [46,] -0.50439883
 [47,] -0.39231020
 [48,] -0.28022157
 [49,] -0.16813294
 [50,] -0.05604431
 [51,]  0.05604431
 [52,]  0.16813294
 [53,]  0.28022157
 [54,]  0.39231020
 [55,]  0.50439883
 [56,]  0.61648746
 [57,]  0.72857608
 [58,]  0.84066471
 [59,]  0.95275334
 [60,]  1.06484197
 [61,]  1.17693060
 [62,]  1.28901922
 [63,]  1.40110785
 [64,]  1.51319648
 [65,]  1.62528511
 [66,]  1.73737374
 [67,]  1.84946237
 [68,]  1.96155099
 [69,]  2.07363962
 [70,]  2.18572825
 [71,]  2.29781688
 [72,]  2.40990551
 [73,]  2.52199413
 [74,]  2.63408276
 [75,]  2.74617139
 [76,]  2.85826002
 [77,]  2.97034865
 [78,]  3.08243728
 [79,]  3.19452590
 [80,]  3.30661453
 [81,]  3.41870316
 [82,]  3.53079179
 [83,]  3.64288042
 [84,]  3.75496905
 [85,]  3.86705767
 [86,]  3.97914630
 [87,]  4.09123493
 [88,]  4.20332356
 [89,]  4.31541219
 [90,]  4.42750081
 [91,]  4.53958944
 [92,]  4.65167807
 [93,]  4.76376670
 [94,]  4.87585533
 [95,]  4.98794396
 [96,]  5.10003258
 [97,]  5.21212121
 [98,]  5.32420984
 [99,]  5.43629847
[100,]  5.54838710

[[24]][[1]]$plot.me
[1] TRUE



[[25]]
[[25]][[1]]
[[25]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[25]][[1]]$scale
[1] TRUE

[[25]][[1]]$se
  [1] 3.67463662 3.60040153 3.52616645 3.45193137 3.37769628 3.30346120
  [7] 3.22922612 3.15499103 3.08075595 3.00652087 2.93228578 2.85805070
 [13] 2.78381562 2.70958054 2.63534545 2.56111037 2.48687529 2.41264020
 [19] 2.33840512 2.26417004 2.18993495 2.11569987 2.04146479 1.96722970
 [25] 1.89299462 1.81875954 1.74452445 1.67028937 1.59605429 1.52181920
 [31] 1.44758412 1.37334904 1.29911396 1.22487887 1.15064379 1.07640871
 [37] 1.00217362 0.92793854 0.85370346 0.77946837 0.70523329 0.63099821
 [43] 0.55676312 0.48252804 0.40829296 0.33405787 0.25982279 0.18558771
 [49] 0.11135263 0.03711754 0.03711754 0.11135263 0.18558771 0.25982279
 [55] 0.33405787 0.40829296 0.48252804 0.55676312 0.63099821 0.70523329
 [61] 0.77946837 0.85370346 0.92793854 1.00217362 1.07640871 1.15064379
 [67] 1.22487887 1.29911396 1.37334904 1.44758412 1.52181920 1.59605429
 [73] 1.67028937 1.74452445 1.81875954 1.89299462 1.96722970 2.04146479
 [79] 2.11569987 2.18993495 2.26417004 2.33840512 2.41264020 2.48687529
 [85] 2.56111037 2.63534545 2.70958054 2.78381562 2.85805070 2.93228578
 [91] 3.00652087 3.08075595 3.15499103 3.22922612 3.30346120 3.37769628
 [97] 3.45193137 3.52616645 3.60040153 3.67463662

[[25]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[25]][[1]]$xlab
[1] "YEAR"

[[25]][[1]]$ylab
[1] "s(YEAR,1)"

[[25]][[1]]$main
NULL

[[25]][[1]]$se.mult
[1] 2

[[25]][[1]]$xlim
[1] 1978 2007

[[25]][[1]]$fit
              [,1]
  [1,] -9.33225806
  [2,] -9.14372760
  [3,] -8.95519713
  [4,] -8.76666667
  [5,] -8.57813620
  [6,] -8.38960573
  [7,] -8.20107527
  [8,] -8.01254480
  [9,] -7.82401434
 [10,] -7.63548387
 [11,] -7.44695341
 [12,] -7.25842294
 [13,] -7.06989247
 [14,] -6.88136201
 [15,] -6.69283154
 [16,] -6.50430108
 [17,] -6.31577061
 [18,] -6.12724014
 [19,] -5.93870968
 [20,] -5.75017921
 [21,] -5.56164875
 [22,] -5.37311828
 [23,] -5.18458781
 [24,] -4.99605735
 [25,] -4.80752688
 [26,] -4.61899642
 [27,] -4.43046595
 [28,] -4.24193548
 [29,] -4.05340502
 [30,] -3.86487455
 [31,] -3.67634409
 [32,] -3.48781362
 [33,] -3.29928315
 [34,] -3.11075269
 [35,] -2.92222222
 [36,] -2.73369176
 [37,] -2.54516129
 [38,] -2.35663082
 [39,] -2.16810036
 [40,] -1.97956989
 [41,] -1.79103943
 [42,] -1.60250896
 [43,] -1.41397849
 [44,] -1.22544803
 [45,] -1.03691756
 [46,] -0.84838710
 [47,] -0.65985663
 [48,] -0.47132616
 [49,] -0.28279570
 [50,] -0.09426523
 [51,]  0.09426523
 [52,]  0.28279570
 [53,]  0.47132616
 [54,]  0.65985663
 [55,]  0.84838710
 [56,]  1.03691756
 [57,]  1.22544803
 [58,]  1.41397849
 [59,]  1.60250896
 [60,]  1.79103943
 [61,]  1.97956989
 [62,]  2.16810036
 [63,]  2.35663082
 [64,]  2.54516129
 [65,]  2.73369176
 [66,]  2.92222222
 [67,]  3.11075269
 [68,]  3.29928315
 [69,]  3.48781362
 [70,]  3.67634409
 [71,]  3.86487455
 [72,]  4.05340502
 [73,]  4.24193548
 [74,]  4.43046595
 [75,]  4.61899642
 [76,]  4.80752688
 [77,]  4.99605735
 [78,]  5.18458781
 [79,]  5.37311828
 [80,]  5.56164875
 [81,]  5.75017921
 [82,]  5.93870968
 [83,]  6.12724014
 [84,]  6.31577061
 [85,]  6.50430108
 [86,]  6.69283154
 [87,]  6.88136201
 [88,]  7.06989247
 [89,]  7.25842294
 [90,]  7.44695341
 [91,]  7.63548387
 [92,]  7.82401434
 [93,]  8.01254480
 [94,]  8.20107527
 [95,]  8.38960573
 [96,]  8.57813620
 [97,]  8.76666667
 [98,]  8.95519713
 [99,]  9.14372760
[100,]  9.33225806

[[25]][[1]]$plot.me
[1] TRUE



[[26]]
[[26]][[1]]
[[26]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[26]][[1]]$scale
[1] TRUE

[[26]][[1]]$se
  [1] 7.633906 7.398010 7.164850 6.934758 6.708079 6.485200 6.266536 6.052507
  [9] 5.843540 5.640075 5.442541 5.251353 5.066911 4.889586 4.719709 4.557570
 [17] 4.403405 4.257391 4.119636 3.990179 3.868986 3.755940 3.650850 3.553462
 [25] 3.463448 3.380416 3.303948 3.233582 3.168826 3.109196 3.054222 3.003436
 [33] 2.956406 2.912759 2.872160 2.834312 2.799000 2.766065 2.735385 2.706900
 [41] 2.680612 2.656549 2.634767 2.615364 2.598450 2.584128 2.572510 2.563703
 [49] 2.557783 2.554805 2.554805 2.557783 2.563703 2.572510 2.584128 2.598450
 [57] 2.615364 2.634767 2.656549 2.680612 2.706900 2.735385 2.766065 2.799000
 [65] 2.834312 2.872160 2.912759 2.956406 3.003436 3.054222 3.109196 3.168826
 [73] 3.233582 3.303948 3.380416 3.463448 3.553462 3.650850 3.755940 3.868986
 [81] 3.990179 4.119636 4.257391 4.403405 4.557570 4.719709 4.889586 5.066911
 [89] 5.251353 5.442541 5.640075 5.843540 6.052507 6.266536 6.485200 6.708079
 [97] 6.934758 7.164850 7.398010 7.633906

[[26]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[26]][[1]]$xlab
[1] "YEAR"

[[26]][[1]]$ylab
[1] "s(YEAR,1.37)"

[[26]][[1]]$main
NULL

[[26]][[1]]$se.mult
[1] 2

[[26]][[1]]$xlim
[1] 1978 2007

[[26]][[1]]$fit
              [,1]
  [1,] -7.52419185
  [2,] -7.32005361
  [3,] -7.11596461
  [4,] -6.91197408
  [5,] -6.70813240
  [6,] -6.50450813
  [7,] -6.30118431
  [8,] -6.09824440
  [9,] -5.89577746
 [10,] -5.69388597
 [11,] -5.49267441
 [12,] -5.29224796
 [13,] -5.09271774
 [14,] -4.89419785
 [15,] -4.69680242
 [16,] -4.50064559
 [17,] -4.30584153
 [18,] -4.11250443
 [19,] -3.92074741
 [20,] -3.73067845
 [21,] -3.54240396
 [22,] -3.35603001
 [23,] -3.17165590
 [24,] -2.98937442
 [25,] -2.80927809
 [26,] -2.63145537
 [27,] -2.45598272
 [28,] -2.28293440
 [29,] -2.11238351
 [30,] -1.94439085
 [31,] -1.77900970
 [32,] -1.61629319
 [33,] -1.45628700
 [34,] -1.29902338
 [35,] -1.14453315
 [36,] -0.99284476
 [37,] -0.84397217
 [38,] -0.69792391
 [39,] -0.55470817
 [40,] -0.41432373
 [41,] -0.27675860
 [42,] -0.14200021
 [43,] -0.01003249
 [44,]  0.11917321
 [45,]  0.24564836
 [46,]  0.36942508
 [47,]  0.49054428
 [48,]  0.60905326
 [49,]  0.72499949
 [50,]  0.83843405
 [51,]  0.94941590
 [52,]  1.05800504
 [53,]  1.16426223
 [54,]  1.26825377
 [55,]  1.37004855
 [56,]  1.46971550
 [57,]  1.56732563
 [58,]  1.66295282
 [59,]  1.75667116
 [60,]  1.84855499
 [61,]  1.93867978
 [62,]  2.02712136
 [63,]  2.11395547
 [64,]  2.19925717
 [65,]  2.28310093
 [66,]  2.36556116
 [67,]  2.44671133
 [68,]  2.52662235
 [69,]  2.60536471
 [70,]  2.68300853
 [71,]  2.75962040
 [72,]  2.83526494
 [73,]  2.91000673
 [74,]  2.98390780
 [75,]  3.05702598
 [76,]  3.12941873
 [77,]  3.20114253
 [78,]  3.27224876
 [79,]  3.34278703
 [80,]  3.41280682
 [81,]  3.48235387
 [82,]  3.55147005
 [83,]  3.62019704
 [84,]  3.68857495
 [85,]  3.75663885
 [86,]  3.82442279
 [87,]  3.89196046
 [88,]  3.95928151
 [89,]  4.02641290
 [90,]  4.09338152
 [91,]  4.16021223
 [92,]  4.22692580
 [93,]  4.29354253
 [94,]  4.36008212
 [95,]  4.42656022
 [96,]  4.49299079
 [97,]  4.55938774
 [98,]  4.62576218
 [99,]  4.69212175
[100,]  4.75847389

[[26]][[1]]$plot.me
[1] TRUE



[[27]]
[[27]][[1]]
[[27]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[27]][[1]]$scale
[1] TRUE

[[27]][[1]]$se
  [1] 4.458032 4.262790 4.070639 3.882120 3.697830 3.518458 3.344777 3.177607
  [9] 3.017825 2.866361 2.724162 2.592167 2.471276 2.362302 2.265907 2.182549
 [17] 2.112423 2.055408 2.011039 1.978528 1.956783 1.944465 1.940084 1.942095
 [25] 1.948936 1.959111 1.971281 1.984240 1.996924 2.008479 2.018231 2.025640
 [33] 2.030325 2.032093 2.030855 2.026627 2.019577 2.009968 1.998125 1.984464
 [41] 1.969486 1.953715 1.937706 1.922049 1.907323 1.894068 1.882788 1.873922
 [49] 1.867810 1.864690 1.864690 1.867810 1.873922 1.882788 1.894068 1.907323
 [57] 1.922049 1.937706 1.953715 1.969486 1.984464 1.998125 2.009968 2.019577
 [65] 2.026627 2.030855 2.032093 2.030325 2.025640 2.018231 2.008479 1.996924
 [73] 1.984240 1.971281 1.959111 1.948936 1.942095 1.940084 1.944465 1.956783
 [81] 1.978528 2.011039 2.055408 2.112423 2.182549 2.265907 2.362302 2.471276
 [89] 2.592167 2.724162 2.866361 3.017825 3.177607 3.344777 3.518458 3.697830
 [97] 3.882120 4.070639 4.262790 4.458032

[[27]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[27]][[1]]$xlab
[1] "YEAR"

[[27]][[1]]$ylab
[1] "s(YEAR,2.19)"

[[27]][[1]]$main
NULL

[[27]][[1]]$se.mult
[1] 2

[[27]][[1]]$xlim
[1] 1978 2007

[[27]][[1]]$fit
              [,1]
  [1,] -4.05882752
  [2,] -3.85152799
  [3,] -3.64437807
  [4,] -3.43752739
  [5,] -3.23112901
  [6,] -3.02539004
  [7,] -2.82056082
  [8,] -2.61689291
  [9,] -2.41465357
 [10,] -2.21414786
 [11,] -2.01568642
 [12,] -1.81958147
 [13,] -1.62615847
 [14,] -1.43574953
 [15,] -1.24868675
 [16,] -1.06529823
 [17,] -0.88590601
 [18,] -0.71083167
 [19,] -0.54039179
 [20,] -0.37487850
 [21,] -0.21457639
 [22,] -0.05976874
 [23,]  0.08928924
 [24,]  0.23236917
 [25,]  0.36924378
 [26,]  0.49970176
 [27,]  0.62357873
 [28,]  0.74071893
 [29,]  0.85097095
 [30,]  0.95422999
 [31,]  1.05041956
 [32,]  1.13946385
 [33,]  1.22131425
 [34,]  1.29597144
 [35,]  1.36344128
 [36,]  1.42373806
 [37,]  1.47692722
 [38,]  1.52309347
 [39,]  1.56232257
 [40,]  1.59473200
 [41,]  1.62047548
 [42,]  1.63970870
 [43,]  1.65259828
 [44,]  1.65935022
 [45,]  1.66017935
 [46,]  1.65530232
 [47,]  1.64496012
 [48,]  1.62941153
 [49,]  1.60891578
 [50,]  1.58374001
 [51,]  1.55416870
 [52,]  1.52048860
 [53,]  1.48298731
 [54,]  1.44195874
 [55,]  1.39769968
 [56,]  1.35050686
 [57,]  1.30067414
 [58,]  1.24849144
 [59,]  1.19424840
 [60,]  1.13823119
 [61,]  1.08071073
 [62,]  1.02195369
 [63,]  0.96222571
 [64,]  0.90177386
 [65,]  0.84082899
 [66,]  0.77962136
 [67,]  0.71836988
 [68,]  0.65726321
 [69,]  0.59648505
 [70,]  0.53621572
 [71,]  0.47660368
 [72,]  0.41777978
 [73,]  0.35987440
 [74,]  0.30299830
 [75,]  0.24722990
 [76,]  0.19264458
 [77,]  0.13931135
 [78,]  0.08726429
 [79,]  0.03652560
 [80,] -0.01288341
 [81,] -0.06096336
 [82,] -0.10773789
 [83,] -0.15323170
 [84,] -0.19747696
 [85,] -0.24053016
 [86,] -0.28245273
 [87,] -0.32330719
 [88,] -0.36316924
 [89,] -0.40212336
 [90,] -0.44025421
 [91,] -0.47764861
 [92,] -0.51439769
 [93,] -0.55059311
 [94,] -0.58632546
 [95,] -0.62167825
 [96,] -0.65673203
 [97,] -0.69156698
 [98,] -0.72625042
 [99,] -0.76083353
[100,] -0.79536648

[[27]][[1]]$plot.me
[1] TRUE



[[28]]
[[28]][[1]]
[[28]][[1]]$x
  [1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
  [9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
 [17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
 [25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
 [33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
 [41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
 [49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
 [57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
 [65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
 [73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
 [81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
 [89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
 [97] 2006.121 2006.414 2006.707 2007.000

[[28]][[1]]$scale
[1] TRUE

[[28]][[1]]$se
  [1] 10.487335 10.234514  9.983272  9.733759  9.486125  9.240537  8.997169
  [8]  8.756191  8.517775  8.282091  8.049302  7.819562  7.593014  7.369790
 [15]  7.150007  6.933766  6.721152  6.512232  6.307056  6.105658  5.908057
 [22]  5.714254  5.524238  5.337992  5.155487  4.976689  4.801568  4.630100
 [29]  4.462261  4.298051  4.137493  3.980627  3.827533  3.678339  3.533217
 [36]  3.392390  3.256161  3.124907  2.999078  2.879219  2.765980  2.660098
 [43]  2.562400  2.473805  2.395289  2.327842  2.272442  2.229989  2.201231
 [50]  2.186706  2.186706  2.201231  2.229989  2.272442  2.327842  2.395289
 [57]  2.473805  2.562400  2.660098  2.765980  2.879219  2.999078  3.124907
 [64]  3.256161  3.392390  3.533217  3.678339  3.827533  3.980627  4.137493
 [71]  4.298051  4.462261  4.630100  4.801568  4.976689  5.155487  5.337992
 [78]  5.524238  5.714254  5.908057  6.105658  6.307056  6.512232  6.721152
 [85]  6.933766  7.150007  7.369790  7.593014  7.819562  8.049302  8.282091
 [92]  8.517775  8.756191  8.997169  9.240537  9.486125  9.733759  9.983272
 [99] 10.234514 10.487335

[[28]][[1]]$raw
 [1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

[[28]][[1]]$xlab
[1] "YEAR"

[[28]][[1]]$ylab
[1] "s(YEAR,1.11)"

[[28]][[1]]$main
NULL

[[28]][[1]]$se.mult
[1] 2

[[28]][[1]]$xlim
[1] 1978 2007

[[28]][[1]]$fit
              [,1]
  [1,] -8.62312353
  [2,] -8.43277139
  [3,] -8.24242900
  [4,] -8.05210610
  [5,] -7.86181268
  [6,] -7.67156252
  [7,] -7.48137242
  [8,] -7.29125927
  [9,] -7.10124129
 [10,] -6.91133988
 [11,] -6.72157695
 [12,] -6.53197461
 [13,] -6.34255702
 [14,] -6.15334933
 [15,] -5.96437672
 [16,] -5.77566511
 [17,] -5.58724146
 [18,] -5.39913286
 [19,] -5.21136649
 [20,] -5.02397005
 [21,] -4.83697143
 [22,] -4.65039850
 [23,] -4.46427910
 [24,] -4.27864103
 [25,] -4.09351209
 [26,] -3.90891990
 [27,] -3.72489156
 [28,] -3.54145405
 [29,] -3.35863430
 [30,] -3.17645841
 [31,] -2.99495194
 [32,] -2.81414048
 [33,] -2.63404894
 [34,] -2.45470106
 [35,] -2.27612044
 [36,] -2.09833043
 [37,] -1.92135278
 [38,] -1.74520862
 [39,] -1.56991904
 [40,] -1.39550381
 [41,] -1.22198118
 [42,] -1.04936933
 [43,] -0.87768579
 [44,] -0.70694582
 [45,] -0.53716413
 [46,] -0.36835532
 [47,] -0.20053180
 [48,] -0.03370444
 [49,]  0.13211593
 [50,]  0.29691975
 [51,]  0.46070016
 [52,]  0.62345068
 [53,]  0.78516522
 [54,]  0.94584066
 [55,]  1.10547526
 [56,]  1.26406731
 [57,]  1.42161714
 [58,]  1.57812788
 [59,]  1.73360285
 [60,]  1.88804616
 [61,]  2.04146545
 [62,]  2.19386936
 [63,]  2.34526664
 [64,]  2.49566882
 [65,]  2.64508983
 [66,]  2.79354369
 [67,]  2.94104569
 [68,]  3.08761461
 [69,]  3.23326977
 [70,]  3.37803080
 [71,]  3.52192036
 [72,]  3.66496279
 [73,]  3.80718244
 [74,]  3.94860527
 [75,]  4.08925985
 [76,]  4.22917500
 [77,]  4.36837996
 [78,]  4.50690636
 [79,]  4.64478665
 [80,]  4.78205330
 [81,]  4.91873994
 [82,]  5.05488139
 [83,]  5.19051251
 [84,]  5.32566836
 [85,]  5.46038456
 [86,]  5.59469683
 [87,]  5.72864086
 [88,]  5.86225169
 [89,]  5.99556391
 [90,]  6.12861212
 [91,]  6.26142977
 [92,]  6.39404814
 [93,]  6.52649819
 [94,]  6.65881029
 [95,]  6.79101060
 [96,]  6.92312351
 [97,]  7.05517331
 [98,]  7.18717996
 [99,]  7.31915808
[100,]  7.45112194

[[28]][[1]]$plot.me
[1] TRUE
for(i in 1:length(gamls)){
  plot(gamls[[i]], main = dls[[i]]$valid_name[1])
}

# species to keep:
ex = ex[c(1,4,12,13,16,18,21,23,26,28)]
d_crop = dplyr::filter(d_crop, valid_name %in% ex)

4.3.2 Build an mvgam model for all species together

4.3.2.1 Prepare the data

# format into long
dat = d_crop |>
  select(valid_name, ABUNDANCE, YEAR) |>
  rename("time" = "YEAR",
         "series" = "valid_name",
         "y" = "ABUNDANCE")
dat$y = as.vector(dat$y)
dat <- filter(dat, series != "Vireo olivaceus")
dat$series <- as.factor(dat$series)
dat$time <- as.integer(dat$time)-min(dat$time)


data_train = dat[which(d_crop$YEAR <= 1999),]
data_test = dat[which(d_crop$YEAR > 2000),]

ggplot(data = data_train) +
  geom_smooth(aes(x = time, y = y, 
                  col = series, fill = series),
              alpha = .1) +
  colorspace::scale_color_discrete_qualitative() +
  colorspace::scale_fill_discrete_qualitative() 
`geom_smooth()` using method = 'loess' and formula = 'y ~ x'

4.3.2.2 Prepare the priors

npops <- length(unique(data_train$series))
knots <- 4

mvgam_prior <- mvgam(
  data = data_train,
  formula = y ~
    s(time, bs = "tp", k = knots) +
    s(series, bs = "re", k = npops),
  family = "poisson",
  trend_model = "GP",
  chains = 3,
  use_stan = TRUE,
  prior_simulation = TRUE
)

test_priors <- get_mvgam_priors(
  y ~ s(time, bs = "tp", k = knots) +
    s(series, bs = "re", k = npops),
  family = "poisson",
  data = data_train,
  trend_model = "GP",
  use_stan = TRUE
)

plot(mvgam_prior, type = "smooths")
4.3.2.2.1 Check the number of knots
knots = 4
npops <- length(unique(data_train$series))

hgam = mgcv::gam(y ~ s(time, bs = "tp", k = 5) + 
                         s(series, bs = 're', k = npops), 
                       family = "poisson",
                       data = data_train)
mgcv::gam.check(hgam)


Method: UBRE   Optimizer: outer newton
full convergence after 10 iterations.
Gradient range [6.015154e-16,1.222171e-06]
(score 2.076686 & scale 1).
Hessian positive definite, eigenvalue range [0.0003777539,0.003389441].
Model rank =  15 / 15 

Basis dimension (k) checking results. Low p-value (k-index<1) may
indicate that k is too low, especially if edf is close to k'.

             k'   edf k-index p-value
s(time)    4.00  1.81    0.93    0.16
s(series) 10.00  8.96      NA      NA
plot(hgam)

4.3.2.3 Train the model on data

#m1 <- mvgam(data = data_train,
              # formula =  y ~ s(time, bs = "tp", k = 5) + 
              #   s(series, bs = "re"),
              # use_lv = FALSE,
              # family = "poisson",
              # trend_model = 'GP',
              # use_stan = TRUE,
              # chains = 2, 
              # burnin = 5000,
              # samples = 10000)

#saveRDS(m1, paste0("variance/outputs/mvgam_variance.rds")) 
m1 <- readRDS(here::here("variance", "outputs", "mvgam_variance.rds"))

4.3.3 Plots and model outputs

4.3.3.1 Visualize model diagnostics and smooths

plot(m1) # Basic model diagnostic plots

mvgam::plot_mvgam_smooth(m1) # Plot estimated smooth functions

mvgam::plot_mvgam_randomeffects(m1) # Plot random effects

dat$series |> unique() # List all unique series included in the dataset
 [1] Agelaius phoeniceus Spinus tristis      Catharus guttatus  
 [4] Setophaga coronata  Setophaga virens    Melospiza melodia  
 [7] Mniotilta varia     Seiurus aurocapilla Turdus migratorius 
[10] Vireo solitarius   
10 Levels: Agelaius phoeniceus Catharus guttatus ... Vireo solitarius

4.3.3.2 Species associations

library(here)
#sp_corr = mvgam::lv_correlations(m1) # Extract latent variable (species) correlation matrix
sp_corr <- readRDS(here::here("variance", "outputs", "sp_corr_variance.rds"))

# name cleanup
colnames(sp_corr$mean_correlations) <- gsub("_", " ", colnames(sp_corr$mean_correlations)) |>
  stringr::str_to_sentence()

rownames(sp_corr$mean_correlations) <- gsub("_", " ", rownames(sp_corr$mean_correlations)) |>
  stringr::str_to_sentence()

4.3.3.3 Plot as a heatmap

Visualize and summarize species (latent variable) correlations from the model

corrplot::corrplot(sp_corr$mean_correlations, 
                   type = "lower",
                   method = "color", 
                   tl.cex = 2.5, cl.cex = 3, tl.col = "black", font = 13)
Warning in corrplot::corrplot(sp_corr$mean_correlations, type = "lower", : Not
been able to calculate text margin, please try again with a clean new empty
window using {plot.new(); dev.off()} or reduce tl.cex
sp_corr$mean_correlations |> mean()
[1] 0.3046276
sp_corr$mean_correlations |> sd()
[1] 0.3740284
sp_corr$mean_correlations |> apply(2, mean) 
    Agelaius phoeniceus     Bombycilla cedrorum     Catharus fuscescens 
             0.18519932              0.16093650              0.19828996 
      Catharus guttatus   Corvus brachyrhynchos     Cyanocitta cristata 
             0.14082619              0.45574604              0.29879417 
      Empidonax alnorum       Empidonax minimus      Geothlypis trichas 
             0.13669726              0.39534503              0.05228182 
   Haemorhous purpureus     Melospiza georgiana       Melospiza melodia 
             0.36583565              0.32710828              0.41040169 
        Mniotilta varia Pheucticus ludovicianus    Poecile atricapillus 
             0.31394922              0.10957683              0.31970726 
    Seiurus aurocapilla  Setophaga caerulescens      Setophaga coronata 
             0.11749735              0.07930013              0.42762314 
 Setophaga pensylvanica     Setophaga ruticilla        Setophaga virens 
             0.39327619              0.26250445              0.32853495 
     Sphyrapicus varius          Spinus tristis      Spizella passerina 
             0.42225813              0.34020221              0.49806301 
Troglodytes troglodytes      Turdus migratorius        Vireo solitarius 
             0.26579594              0.50849813              0.48569396 
 Zonotrichia albicollis 
             0.52962935 
sp_corr$mean_correlations |> apply(2, sd) |> lines()

sp_corr$mean_correlations |> hist()

4.4 Step 4: Box 3 - Prediction

4.4.1 Process the data

Here we use d_crop, previously processed in Box 2, and further prepare it for this section.

# Add a rare/undersampled species for Example 1
d_crop_rare <- readRDS(here::here("prediction", "example_rare_species.rds"))

d_crop_merged <- rbind(d_crop, d_crop_rare)

# Rename columns and adjust abundance
dat <- d_crop_merged %>%
  rename(
    y = ABUNDANCE,
    series = valid_name, # for the mvgam requirement
    lat = LATITUDE,
    long = LONGITUDE,
    time = YEAR # for the mvgam requirement
  )

dat <- dat %>%
  group_by(time) %>%
  mutate(total_abun = sum(y)) %>%
  mutate(rel_abun = y / total_abun) %>%
  select(-total_abun)

4.4.1.1 mvgam format requirements

Prepare and format the dataset for HGAM fitting and forecasting: adjust columns to meet mvgam requirements, define training/testing subsets, and create datasets with and without specific species for out-of-sample forecasts.

## Adjust columns for mvgam requirements
dat$y <- as.vector(dat$y)
dat <- filter(dat, series != "Vireo olivaceus")
dat$series <- as.factor(dat$series)
dat$time <- as.integer(dat$time) - min(dat$time)

# Subset the data in training and testing folds
data_train <- dat[which(d_crop$YEAR <= 1999), ]
data_test <- dat[which(d_crop$YEAR > 2000), ]

# subsetting the data with and without a species for out-of-sample forecasting
# Remove Setophaga pinus due to missing observations in some years

data_noMniotilta <- filter(dat, series != "Mniotilta varia" & series != "Setophaga pinus")
data_Mniotilta <- filter(dat, series == "Mniotilta varia")

4.4.2 Fit Models

4.4.2.1 Inspect and visualize training and testing data

Finalize and visualize data subsets: unused factor levels are removed, the temporal extent of the test set is verified, and all series are plotted to assess coverage between training and testing periods.

set.seed(2505)

data_train <- data_train %>%
  droplevels()
data_test <- data_test %>%
  droplevels()

range(data_test$time)
[1] 23 29
# Plot series
plot_mvgam_series(
  data = data_train,
  newdata = data_test,
  series = "all"
)

4.4.2.2 Penalized splines forecast: mod_forecast_ps

A State-Space hierarchical GAM is fitted using a Poisson family, AR(1) temporal dynamics, and penalized spline smooths. The model structure incorporates hierarchical time effects for computational efficiency and summarizes key outputs excluding beta estimates.

# Set up a State-Space hierarchical GAM with AR1 dynamics for autocorrelation
# Smooths are penalized splines
# mod_forecast_ps <- mvgam(
#   data = data_train,
#   formula = y ~
#     s(series, bs = "re"),
# 
#   # Hierarchical smooths of time set up as a
#   # State-Space model for sampling efficiency
#   trend_formula = ~
#     s(time, bs = "tp", k = 6) +
#       s(time, trend, bs = "sz", k = 6),
#   family = poisson(),
# 
#   # AR1 for "residual" autocorrelation
#   trend_model = AR(p = 1),
#   noncentred = TRUE,
#   priors = prior(exponential(2),
#     class = sigma
#   ),
#   backend = "cmdstanr"
# )

# Read the model
mod_forecast_ps <- readRDS(here::here("prediction", "output", "mod_nick.rds"))
4.4.2.2.1 Model summary
summary(mod_forecast_ps, include_betas = FALSE)
GAM observation formula:
y ~ +s(series, bs = "re")

GAM process formula:
~s(time, bs = "tp", k = 6) + s(time, trend, bs = "sz", k = 6)

Family:
poisson

Link function:
log

Trend model:
AR(p = 1)

N process models:
10 

N series:
10 

N timepoints:
22 

Status:
Fitted using Stan 
4 chains, each with iter = 1000; warmup = 500; thin = 1 
Total post-warmup draws = 2000


GAM observation model coefficient (beta) estimates:
            2.5% 50% 97.5% Rhat n_eff
(Intercept) -1.1 2.7   6.1    1  1516

GAM observation model group-level estimates:
                 2.5%    50% 97.5% Rhat n_eff
mean(s(series)) -1.90 -0.025   1.9    1  3102
sd(s(series))    0.45  0.750   1.4    1   757

Approximate significance of GAM observation smooths:
           edf Ref.df Chi.sq p-value
s(series) 8.88     10   85.8     0.1

Process model AR parameter estimates:
          2.5%      50% 97.5% Rhat n_eff
ar1[1]  -0.072  0.52000  0.94 1.01   522
ar1[2]  -0.590 -0.00310  0.68 1.00   521
ar1[3]  -0.710  0.35000  0.94 1.00   869
ar1[4]  -0.370  0.33000  0.89 1.00   840
ar1[5]  -0.820  0.00970  0.88 1.00   948
ar1[6]  -0.350  0.25000  0.87 1.00   500
ar1[7]  -0.860  0.06900  0.91 1.00  1301
ar1[8]  -0.900 -0.02100  0.91 1.01  1295
ar1[9]  -0.480  0.21000  0.85 1.01   749
ar1[10] -0.780  0.00031  0.89 1.00  1609

Process error parameter estimates:
            2.5%  50% 97.5% Rhat n_eff
sigma[1]  0.3100 0.47  0.71 1.00   876
sigma[2]  0.2500 0.41  0.65 1.00   705
sigma[3]  0.0097 0.21  0.46 1.00   376
sigma[4]  0.1600 0.41  0.73 1.00   766
sigma[5]  0.0076 0.14  0.31 1.00   497
sigma[6]  0.2500 0.43  0.68 1.00   748
sigma[7]  0.0033 0.10  0.30 1.00   624
sigma[8]  0.0058 0.17  0.53 1.01   665
sigma[9]  0.0740 0.17  0.30 1.00   843
sigma[10] 0.0047 0.10  0.30 1.00   821

GAM process model coefficient (beta) estimates:
                  2.5%   50% 97.5% Rhat n_eff
(Intercept)_trend -3.5 0.057   3.7    1  1530

Approximate significance of GAM process smooths:
                 edf Ref.df Chi.sq p-value   
s(time)        0.584      5   9.56  0.0038 **
s(time,series) 1.256     54  10.22  1.0000   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Stan MCMC diagnostics:
n_eff / iter looks reasonable for all parameters
Rhat looks reasonable for all parameters
0 of 2000 iterations ended with a divergence (0%)
1106 of 2000 iterations saturated the maximum tree depth of 10 (55.3%)
 *Run with max_treedepth set to a larger value to avoid saturation
E-FMI indicated no pathological behavior

Samples were drawn using NUTS(diag_e) at Wed Oct 15 1:39:31 PM 2025.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split MCMC chains
(at convergence, Rhat = 1)
4.4.2.2.2 Plots
# Plot random effects
mvgam::plot_mvgam_randomeffects(mod_forecast_ps)

# Condtional effects
conditional_effects(mod_forecast_ps)

# Forecast penalized splines
forecast_penalized_splines <- plot_predictions(
  mod_forecast_ps,
  by = c("time", "series", "series"),
  newdata = datagrid(
    time = 1:max(data_test$time),
    series = unique
  ),
  type = "expected"
)
forecast_penalized_splines

Obviously the splines show high extrapolation uncertainty into the test time points, but that is ok as it isn’t the focus of this exercise. But if we wanted better forecasts, let’s use GPs in place of the penalized smooths. Source used.

4.4.2.2.3 Look at some of the AR1 estimates
# Look at some of the AR1 estimates
mcmc_plot(mod_forecast_ps, variable = "ar1", regex = TRUE)

4.4.2.3 Gaussian process forecasts : mod_forecast_GP

This model replaces penalized spline smooths with Gaussian Process terms to more flexibly model temporal dependencies and enhance forecasting accuracy.

# Using Gaussian Process in place of penalized smooths to get better forecasts
# mod_forecast_GP <- mvgam(
#   data = data_train,
#   formula = y ~
#     s(series, bs = "re"),
# 
#   # Hierarchical smooths of time set up as a
#   # State-Space model for sampling efficiency
#   trend_formula = ~
#     gp(time, k = 6) +
#       s(time, trend, bs = "sz", k = 6),
#   family = poisson(),
# 
#   # AR1 for "residual" autocorrelation
#   trend_model = AR(p = 1),
#   noncentred = TRUE,
#   priors = prior(exponential(2),
#     class = sigma
#   ),
#   backend = "cmdstanr"
# )

# Read the model
mod_forecast_GP <- readRDS(here::here("prediction", "output", "mod_nick_GP.rds"))
4.4.2.3.1 Model summary
summary(mod_forecast_GP, include_betas = FALSE)
4.4.2.3.2 Predict
# # Build prediction grid
# pred_data <- data.frame(
#   time = rep(1:max(data_test$time), each = length(unique(data_train$series))),
#   series = rep(unique(data_train$series), times = max(data_test$time))
# )
# 
# predictions <- predictions(
#   mod_forecast_GP,
#   newdata = pred_data,
#   by = c("time", "series", "series"),
#   type = "expected"
# )
# 
# # Mark which points are forecasts & Add a vertical line where the train test splits (time = 22)
# predictions$forecast <- ifelse(predictions$time > 22, "Forecast", "Fitted")
4.4.2.3.3 Plot species-level forecasts
# ggplot(predictions, aes(x = time, y = estimate)) +
#   geom_ribbon(
#     aes(ymin = conf.low, ymax = conf.high, fill = series),
#     alpha = 0.2
#   ) +
#   geom_line(
#     data = subset(predictions, forecast == "Fitted"),
#     aes(color = series), linewidth = 1
#   ) +
#   geom_line(
#     data = subset(predictions, forecast == "Forecast"),
#     aes(color = series), linewidth = 1, linetype = "dashed"
#   ) +
#   geom_vline(xintercept = 22, linetype = "dotted") +
#   geom_point(data = data_train, aes(x = time, y = y), alpha = 0.2) +
#   geom_point(data = data_test, aes(x = time, y = y), alpha = 0.2) +
#   facet_wrap(~series, scales = "free_y") +
#   theme(
#     legend.position = "none",
#     strip.text = element_text(size = 14, face = "italic")
#   ) +
#   labs(y = "Abundance", x = "Time") +
#   theme(axis.title = element_text(size = 14))
4.4.2.3.4 Plot latent/global trend
# plot_predictions(
#   mod_nick_GP,
#   by = c("time"),
#   newdata = datagrid(
#     time = 1:max(data_test$time),
#     series = unique
#   ),
#   type = "expected"
# ) +
#   geom_vline(xintercept = 22, linetype = "dotted") +
#   labs(y = "Global latent trend", x = "Time") +
#   theme(axis.title = element_text(size = 14))

4.4.3 Gaussian process - predicting new species

4.4.3.1 Black-and-white Warbler (BAWW) Post-stratification model

4.4.3.1.1 Training dataset & train the model

In this section, we prepare a training dataset that excludes Mniotilta varia (Black-and-white Warbler) to perform post-stratification. We examine missing observations across species and time, verify data completeness, and then load the fitted state-space HGAM (Gaussian Process–based) trained on the reduced dataset.

# # Black-and-white Warbler Post-stratification Model ----
# # Create training data excluding Mniotilta varia (Black-and-white Warbler)
# data_train_noBAWW <- data_noMniotilta %>%
#   droplevels()
# 
# # Set up State-Space hierarchical GAM excluding BAWW for post-stratification
# set.seed(2505)
# data_train_noBAWW %>%
#   group_by(series) %>%
#   summarise(
#     n_obs = n(),
#     expected_obs = length(unique(data_train_noBAWW$time)),
#     missing_obs = expected_obs - n_obs
#   ) %>%
#   filter(missing_obs > 0)
# unique(data_train_noBAWW$series)
# 
# 
# colSums(is.na(data_train_noBAWW))

# mod_strat_BAWW <- mvgam(
#   data = data_train_noBAWW,
#   formula = y ~
#     s(series, bs = "re"),
# 
#   # Hierarchical smooths of time set up as a
#   # State-Space model for sampling efficiency
#   trend_formula = ~
#     gp(time, k = 3, gr = FALSE),
#   family = poisson(),
# 
#   # AR1 for "residual" autocorrelation
#   trend_model = AR(p = 1),
#   noncentred = TRUE,
#   priors = prior(exponential(2),
#     class = sigma
#   ),
#   backend = "cmdstanr"
# )

# Read the model
# mod_strat_BAWW <- readRDS(here::here("prediction", "output", "mod_strat_BAWW.rds"))
4.4.3.1.2 Construct weighted prediction data for post-stratification
# # Post-stratification for Black-and-white Warbler prediction ---
# # predict trends for all species and weight these based
# # on their "distance" to the new species
# unique_species_noBAWW <- levels(data_train_noBAWW$series)
# 
# # Add some weights; here a higher value means that species is "closer" to the
# # un-modelled target species. This could for example be the inverse of a phylogenetic
# # or functional distance metric
# 
# # Initialize all weights to 1
# species_weights_BAWW <- rep(1, length(unique_species_noBAWW))
# names(species_weights_BAWW) <- unique_species_noBAWW
# 
# # Assign higher weight to warblers species
# # Weight it 10x higher than other species for strong post-stratification
# 
# setophaga_species <- grep("Setophaga", unique_species_noBAWW, value = TRUE)
# species_weights_BAWW[setophaga_species] <- 10
# species_weights_BAWW["Seiurus aurocapilla"] <- 10
# 
# 
# # Generate the prediction grid; here we replicate each species' temporal grid
# # a number of times, with the number of replications determined by the weight
# # vector above
# pred_dat_BAWW <- do.call(
#   rbind,
#   lapply(seq_along(unique_species_noBAWW), function(sp) {
#     sp_name <- unique_species_noBAWW[sp]
#     weight <- species_weights_BAWW[sp_name]
# 
#     do.call(
#       rbind,
#       replicate(
#         weight,
#         data.frame(
#           time =
#             1:max(data_train_noBAWW$time + 1), # time is indexed starting at 0
#           series = sp_name
#         ),
#         simplify = FALSE
#       )
#     )
#   })
# ) %>%
#   dplyr::mutate(
#     series = factor(series, levels = levels(data_train_noBAWW$series))
#   )
4.4.3.1.3 Get post-stratified predictions
# Generate post-stratified predictions for Black-and-white Warbler
# Marginalize over "time" to compute weighted average predictions
# post_strat_BAWW <- marginaleffects::avg_predictions(
#   mod_strat_BAWW,
#   newdata = pred_dat_BAWW,
#   by = "time",
#   type = "expected"
# )
4.4.3.1.4 Visualize post-stratified predictions for BAWW

We compare the post-stratified predictions for Mniotilta varia (Black-and-white Warbler) with the observed abundance data from the original dataset. The plot displays the predicted trend with 95% credible intervals (shaded area) alongside the empirical observations, allowing for a visual assessment of how well the post-stratified model captures the species’ temporal dynamics.

# Visualization: Post-stratified BAWW predictions ----
# Plot the post-stratified trend predictions for Black-and-white Warbler
# Compare with actual BAWW data from the original dataset
# actual_BAWW_data <- dat %>%
#   filter(series == "Mniotilta varia")

# plot_BAWW_poststrat <- ggplot(post_strat_BAWW, aes(x = time, y = estimate)) +
#   geom_ribbon(aes(ymax = conf.high, ymin = conf.low),
#     colour = NA, fill = "steelblue", alpha = 0.4
#   ) +
#   geom_line(colour = "steelblue", linewidth = 1.2) +
#   geom_point(
#     data = actual_BAWW_data,
#     aes(x = time, y = y),
#     colour = "black", alpha = 0.7, size = 2
#   ) +
#   theme_classic() +
#   labs(
#     y = "Abundance (Black-and-white Warbler)",
#     x = "Time"
#   ) +
#   theme(
#     plot.title = element_text(size = 12),
#     plot.subtitle = element_text(size = 10)
#   )
# 
# print(plot_BAWW_poststrat)
4.4.3.1.5 Anchor and evaluate Post-stratified predictions for BAWW model

To align the post-stratified forecasts with observed data, we anchor the predictions by calibrating the intercept using the first year of Mniotilta varia (Black-and-white Warbler) observations. The offset ensures that predicted abundances match the empirical baseline. We then assess model performance using MAE and RMSE, and compare prediction agreement with a standard GAM by examining correlation and directional trend consistency between the two models.

# # Anchored Post-stratified BAWW Model ----
# # Use first year of BAWW data to calibrate the intercept of post-stratified predictions
# 
# # Get the first year BAWW observation for anchoring
# first_year_BAWW <- actual_BAWW_data %>%
#   filter(time == 0)
# 
# # Find the post-stratified prediction for the same time point
# first_year_pred <- post_strat_BAWW %>%
#   filter(time == 1)
# 
# # Calculate the offset needed to match observed abundance
# abundance_offset <- first_year_BAWW$y - first_year_pred$estimate
# 
# # Apply offset to all post-stratified predictions
# post_strat_BAWW_anchored <- post_strat_BAWW %>%
#   mutate(
#     estimate_original = estimate,
#     conf.low_original = conf.low,
#     conf.high_original = conf.high,
#     estimate = estimate + abundance_offset,
#     conf.low = conf.low + abundance_offset,
#     conf.high = conf.high + abundance_offset
#   )
# 
# mvgam_pred_mean <- post_strat_BAWW_anchored$estimate
# mae_mvgam <- mean(abs(data_Mniotilta$y - mvgam_pred_mean))
# rmse_mvgam <- sqrt(mean((data_Mniotilta$y - mvgam_pred_mean)^2))
# 
# 
# # GAM for BAWW
# BAWW_gam <- gam(y ~ s(time), data = data_Mniotilta)
# 
# 
# # Calculate correlation between predictions
# cor_predictions <- cor(mvgam_pred_mean, gam_pred)
# cor_predictions
# 
# # Direction of trend agreement
# gam_trend_direction <- sign(diff(gam_pred))
# mvgam_trend_direction <- sign(diff(mvgam_pred_mean))
# trend_agreement <- mean(gam_trend_direction == mvgam_trend_direction)
# trend_agreement
4.4.3.1.6 Visualize anchored versus original post-stratified predictions

This plot compares the anchored post-stratified predictions for Mniotilta varia (Black-and-white Warbler) with the observed abundance data. The anchored model, shown with a dashed green line and shaded credible interval, represents predictions adjusted to match the observed baseline, allowing visual assessment of the calibration effect relative to the original post-stratified estimates.

# Visualization: Anchored vs Original Post-stratified Predictions ----
# plot_BAWW_anchored <- ggplot() +
#   # Anchored post-stratified prediction
#   geom_ribbon(
#     data = post_strat_BAWW_anchored,
#     aes(x = time, ymin = conf.low, ymax = conf.high),
#     fill = "darkgreen", alpha = 0.4
#   ) +
#   geom_line(
#     data = post_strat_BAWW_anchored,
#     aes(x = time, y = estimate),
#     color = "darkgreen", size = 1.2, linetype = "dashed"
#   ) +
# 
#   # Actual BAWW data
#   geom_point(
#     data = actual_BAWW_data,
#     aes(x = time, y = y),
#     colour = "black", alpha = 0.2, size = 2.5
#   ) +
#   theme_classic() +
#   labs(
#     y =
#       expression(paste("Predicted ", italic("Mniotilta varia"), " abundance")),
#     x = "Time"
#   ) +
#   theme(
#     axis.title = element_text(size = 12),
#     legend.position = "none"
#   )

5 References

Clark, N. (2023). Temporal autocorrelation in GAMs and the mvgam package. https://ecogambler.netlify.app/blog/autocorrelated-gams/

Pardieck, K. L., Ziolkowski Jr., D. J., and Hudson, M. A. R. (2015). North American Breeding Bird Survey Dataset 1966 - 2014, version 2014.0. https://biotime.st-andrews.ac.uk/selectStudy.php?study=195

Pedersen, E. J., Miller, D. L., Simpson, G. L., & Ross, N. (2019). Hierarchical generalized additive models in ecology: an introduction with mgcv. PeerJ, 7, e6876.

Pedersen, E. J., Koen-Alonso, M., & Tunney, T. D. (2020). Detecting regime shifts in communities using estimated rates of change. ICES Journal of Marine Science, 77(4), 1546-1555